Sylvester's sequence

Question

Sylvester's sequence, OEIS A000058, is an integer sequence defined as follows:

Each member is the product of all previous members plus one. The first member of the sequence is 2.

Task

Create a program to calculate the nth term of Sylvester's Sequence. Standard input, output and loopholes apply.

Standard sequence rules apply.

This is code-golf, so the goal is to minimize the size of your source code as measured in bytes.

Test Cases

You may use either zero or one indexing. (Here I use zero indexing)

>>0
2
>>1
3
>>2
7
>>3
43
>>4
1807

Answer 1

Python 2, 87 73 64 60 51 bytes

14 23 25 bytes saved thanks to Leaky Nun

9 bytes saved thanks to Specter Terrasbane

Here's my go at my own challenge.

f=lambda x:reduce(int.__mul__,[1]+map(f,range(x)))+1

Answer 2

Haskell, 27 bytes

f 0=2
f n=f(n-1)^2-f(n-1)+1

Try it online!

Not the shortest Haskell answer but it uses a new method.

Answer 3

Flurry, 26 bytes

{}[(<><<>()>)({})]{{}}{}{}

Verification

$ echo -n "{}[(<><<>()>)({})]{{}}{}{}" | wc -c
26
$ ./flurry -nin -c "{}[(<><<>()>)({})]{{}}{}{}" 0
2
$ ./flurry -nin -c "{}[(<><<>()>)({})]{{}}{}{}" 1
3
$ ./flurry -nin -c "{}[(<><<>()>)({})]{{}}{}{}" 2
7
$ ./flurry -nin -c "{}[(<><<>()>)({})]{{}}{}{}" 3
43
$ ./flurry -nin -c "{}[(<><<>()>)({})]{{}}{}{}" 4
1807

How it works

We have a formula \$a(n+1) = a(n) (a(n) - 1) + 1\$, but pred is well-known to be expensive in SKI calculus, so I defined an auxiliary sequence:

$$ b(n) = a(n)-1 \\ a(n+1) - 1 = (a(n)-1+1)(a(n)-1) \\ b(n+1) = b(n)(b(n)+1), b(0) = 1 $$

Then we can use the nature of Church numerals to calculate the \$n\$-th term as

b = \n. n (\x. x ∘ succ x) 1
a = \n. succ (b n)
  = \n. succ (n (\x. x ∘ succ x) 1)

where succ is the successor function and ∘ is function composition (which acts as multiplication when given two Church numerals).

We can represent the \x. x ∘ succ x part directly in Flurry as {<({})[<><<>()>{}]>}, but we can do better. We can try converting to SKB:

\x. \f. x (succ x f)
\x. \f. K x f (succ x f)
\x. S (K x) (succ x)
\x. (S∘K) x (succ x)
S (S∘K) succ
succ succ  (because succ = S (S∘K))

So we can duplicate succ via the stack, making it [(<><<>()>){}] (-6 bytes). Using it in the full program, we get:

\n. succ (n (\x. x ∘ succ x) 1)
\n. succ (n (succ succ) 1)

<><<>()>[       succ (
 {}[              n (
    (<><<>()>)       succ [push succ]
    {}               succ [pop]
   ]                )
 {}               I [pop from empty stack]
]               )

But I wasn't satisfied because it still has two copies of succ. So I changed the "calculate b(n) and apply succ on it" to "apply succ b(n) times to 1", which gives

\n. n (succ succ) 1 succ 1

{}[           n (
  (<><<>()>)    succ [push succ]
  ({})          succ [pop and push succ]
  ]           )
{{}}          I    [1]
{}            succ [pop]
{}            I    [pop from empty stack]

Answer 4

Ruby, 29 bytes

f=->a{a<1?2:(b=f[a-1])*~-b+1}

+2 for adding f= to byte count.

-2 from Dingus's suggestion.

Try it online!

Answer 5

Vyxal, 7 bytes

-2 bytes thanks to Steffan

2$(:‹*›

Explanation:

2$(:‹*›
2$          Push 2 and swap it with the input
   (:       Loop through input and duplicate value
     ‹*     Decrement the value and multiply
       ›    Increment value

Try it Online!

Answer 6

Julia 1.0, 27 22 bytes

~x=*(1,.~(0:x-1)...)+1

Try it online!

-5 bytes (!!) thanks to MarcMush: Replace prod() with *(); also, pad the argument list with 1 to avoid handling \$a_0\$ as a special case

Answer 7

Actually, 14 12 bytes

This used 0-indexing. Golfing suggestions welcome. Try it online!

2#,`;πu@o`nF

Ungolfing:

2#              Start with [2]
  ,`     `n     Take 0-indexed input and run function (input) times
    ;           Duplicate list
     πu         Take product of list and increment
       @o       Swap and append result to the beginning of the list
           F    Return the first item of the resulting list

Answer 8

GolfScript, 12 10 bytes

2 bytes thanks to Dennis.

~2\{.(*)}*

Try it online!

Uses a(n) = a(n-1) * (a(n-1)-1) + 1.

Answer 9

MATL, 12 bytes

This can definitely be golfed further

Hiq:"tpQh]0)

This solution uses 1-based indexing.

Try it online!

Answer 10

PowerShell v2+, 56 bytes

param($n)$a=,2;0..$n|%{$a+=($a-join'*')+'+1'|iex};$a[$n]

Iterative version. Takes input, sets the first value in our array $a, loops. Each loop we take all of $a, -join them together with *, tack on a +1, and pipe to Invoke-Expression (similar to eval). That's stored as a new value on the end of $a. Then, we just index into $a for the requested number.

Calculates one index higher than necessary, which shouldn't be a problem. Output is solid until you reach the limits of round-trip precision issues and/or formatting issues where PowerShell converts to scientific notation.

PS C:\Tools\Scripts\golfing> 0..10|%{"$_ -> "+(.\sylvesters-sequence.ps1 $_)}
0 -> 2
1 -> 3
2 -> 7
3 -> 43
4 -> 1807
5 -> 3263443
6 -> 10650056950807
7 -> 1.13423713055422E+26
8 -> 1.28649386832787E+52
9 -> 1.65506647324521E+104
10 -> 2.73924503086033E+208

---

The recursive version is one byte longer, at 57 bytes, using PowerShell's equivalent of a lambda -- $x={param($n)if(!$n){2}else{(&$x(--$n))*((&$x($n))-1)+1}}. Call it via something like &$x(4)

---

You could tack on a [bigint] for the iex expression to carry forward the good precision as follows -- param($n)$a=,2;0..$n|%{$a+='[bigint]"'+($a-join'"*"')+'"+"1"'|iex};$a[$n] for 73 bytes (corrected thanks to Brad Gilbert b2gills).

PS C:\Tools\Scripts\golfing> 0..10|%{"$_ -> "+(.\sylvesters-sequence.ps1 $_)}
0 -> 2
1 -> 3
2 -> 7
3 -> 43
4 -> 1807
5 -> 3263443
6 -> 10650056950807
7 -> 113423713055421844361000443
8 -> 12864938683278671740537145998360961546653259485195807
9 -> 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
10 -> 273924503086030314234102342916746862811943643675809146279473679416086920262269936343321184045824386349295487372839923697584879743063177305807538834294603
44956410077034761330476016739454649828385541500213920807

Answer 11

PARI/GP, 29 25 bytes

a(n)=prod(i=0,n-1,a(i))+1

Thanks to alephalpha for shaving off 4 bytes.

Answer 12

Maple 35 bytes

f:=n->`if`(n>0,f(n-1)^2-f(n-1)+1,2)

Usage:

> f:=n->`if`(n>0,f(n-1)^2-f(n-1)+1,2):
> seq(f(i),i=0..4);
  2, 3, 7, 43, 1807

Answer 13

Javascript (ES6), 25 bytes

f=n=>n--?(n=f(n))*--n+1:2

Returns:

• the exact result for n=0 to n=6
• an approximated value for n=7 to n=10
• Infinity for n>10

f=n=>n--?(n=f(n))*--n+1:2

console.log(f(0))
console.log(f(1))
console.log(f(2))
console.log(f(3))
console.log(f(4))
console.log(f(5))
console.log(f(6))
console.log(f(7))

Answer 14

Retina, 43 26 bytes

Input and output are in unary (input in 1's, output in x's.) The result is computed using a(n+1) = a(n) * (a(n) - 1) + 1, iterated n times.

^
xx
{`x(?=.*1)
$`$`
x1
xx

Try it online

Input and output in decimal (53 36 bytes):

.*
$*
^
xx
{`x(?=.*1)
$`$`
}`x1
xx
.

Try it online

Thanks to Martin for golfing 17 bytes

Answer 15

Dyalog APL, 15 bytes

{×⍵:1+×/∇¨⍳⍵⋄2}

×⍵: if the argument is grater than zero:
  1+ one plus
  ×/ the product of
  ∇¨ this function applied to each of
  ⍳⍵ first n integers (beginning with zero)
⋄ else:
  2 return two

0-based indexing – needs ⎕IO←0.

TryAPL online!

Answer 16

Pip, 11 bytes

Lao*:o+1o+1

The shortest way I've found so far. Uses the formula from Martin's Hexagony answer: define b(0) = 1, b(n) = b(n-1) * (b(n-1) + 1), and then a(n) = b(n) + 1.

La           Loop number of times equal to cmdline input:
  o*:o+1     Multiply o by o+1 in place (o is a variable preinitialized to 1)
        o+1  Output o+1

Try it online!

Answer 17

Perl, 28 26 23 22 bytes

Includes +1 for -p

Run with the input (with 1-based indexing) on STDIN:

sylvester.pl <<< 5

sylvester.pl:

#!/usr/bin/perl -p
$.*=$_=$.+1for($_)x$_

Answer 18

R, 56 49 bytes

n=scan();x=2;for(i in 1:n){x=c(x,prod(x)+1)};cat(x[n+1])

Ungolfed:

n=scan()            # Take input n
x=2                 # Initialize sequence to 2
for(i in 1:n){
  x=c(x,prod(x)+1)  # Append the product of the previous numbers + 1
}
cat(x[n+1])         # Print the nth + 1 number in seq

Slightly golfed thanks to @Frédéric:

n=scan();x=2;for(i in 1:n)x=c(x,prod(x)+1);x[n+1]

Answer 19

Python 3, 71 69 68 63 57 bytes

Python 3, 71 69 68 bytes

l=[2]
for _ in range(int(input())):
    n=1
    for i in l:n*=i
    l+=[n+1]
print(l[-1])

Also 68 bytes:

l=[2]
a=int(input())
while len(l)<a:
    n=1
    for i in l:n*=i
    l+=[n+1]
print(l[-1])

EDIT:

Thanks @WheatWizard for pointing out about using n instead of no, and removing the space between for i in l and n*=i.

Also thanks for pointing out about moving int(input()) into the range function.

EDIT 2:

Thanks @WheatWizard for pointing out the iteration tip, it has allowed me to write these two, shorter, programs:

Python 3, 63 bytes

l=[2]
for _ in"a"*int(input()):
    n=1
    for i in l:n*=i
    l+=[n+1]
print(l[-2])

Python 3, 57 bytes

l=[2]
for _ in"a"*int(input()):
    b=l[-1]
    l+=[(b-1)*b+1]
print(b)

The second code (57 bytes) does not follow the instructions for making the sequence (i.e: product of the sequence+1) instead it works on the fact that the last number will always be the product of the rest+1 meaning that instead of iterating through the sequence, I can multiply the last number by itself-1 and then add 1 back on.

Answer 20

dc, 34 bytes

0sg[[d1-*1+Lgx]Sg1-d0<f]dsfx2Lgx++

This pops the argument from top of stack, and pushes the result to stack, as normal for dc.

Annotated full program

#!/usr/bin/dc

# accept input
?

# initialise the bottom of the g-stack
0sg
# Add n iterations of recurrence formula
[[d1-*1+Lgx]Sg1-d0<f]dsfx
# Prime the 0th value
2
# Execute all of the g-stack
Lgx
# Last instruction left a zero on the stack
+
# Special case: if input is 0, f left a -1 behind.  This is a correction
# for wrongly doing 2->3 in that case
+

# print output
p

It works by using the recurrence relation described in OEIS: a[n+1] = a[n]² - a[n] + 1, starting with a[0]==2. Equivalently, a[n+1] = a[n](a[n]-1) + 1, written in dc as d1-*1+.

We push n copies of the program d1-*1+ to the stack g, prime the main stack with the initial value 2, and set off. There's a correction for n=0, because we always push at least one instance of the recurrence. Handily, we can fix that, because function f leaves -1 on the stack in that case, and 0 otherwise.

Test output:

0: 2
1: 3
2: 7
3: 43
4: 1807
5: 3263443
6: 10650056950807
7: 113423713055421844361000443
8: 12864938683278671740537145998360961546653259485195807
9: 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443
10: 27392450308603031423410234291674686281194364367580914627947367941608692026226993634332118404582438634929548737283992369758487974306317730580753883429460344956410077034761330476016739454649828385541500213920807
11: 750346333909286311464218348364293017384724140073732363176684391768374238237200233203724274839819736227493060107386942069521875902258281351952761393460726027774387698896086030486687796275661950199835484418384103096899499524666007073298797852932127876923983340497448231960048833094195425231846478785035602339261149953564729371337917773386670133413581537490788020231265093210310224397095644371148893261284201611453610443
12: 563019620811106188735345793029131127645126456201508328395934709948713369875017428398616526515350801978901280848429236023780360625686785326318172135941491985234945009397938528773976977887356630327917721419666751591559883455828027643329740930320548089836575156581070880066847294722353255119648341271402723167206816552066010592134725124376810874159292118224274440907862996344067325025151751506647339684959479438354192989470470488621172745980086435801519575581664038703641801974453354864238123148678312993828328158261237284571445163949954735321181426755485563860804935755099928085508785637606452207007984638610604113718738727804169240213041488645142155664706600019329809186121988322464207409749450811638629159492106903853533242008723387118397794980575878357156285111258733862431522178328441469980110808406224908967784943255608168545045807
13: 316991093418281796980738587324498503465985663563441351614965595710659626509023026378810664917769979749230375616949095839488230630774365784766585678394020150307543448990686716629735821013846949520218610883960194258122308878890968113466913053158083723070515602776324450012006168592325685889943262781933132780014500164781142497008320197365141855119010118077705678576368755229432787283587491897170937657553086679827144799087397199129432233281774986701578182361474362882421927116451702868297347253630717771757957438615228337552613006602138504913204731416596016919892552584014059657038635241014722034375088903021315484876024289828564177721518967548558336213757430766087730295001595138792039193609746512786881659903942227205537012891959828532940594409566163694454653037016800027294499421291400492041597627904670868358757293568071192353450861046220903121264904877170553117406388566305811088048722332066039563082830094354238880920553702156022717609505663704069061610519598560624334935881397512984533454362321248854729174814176943381209734396537109715522733592519084452225492188715705481658124794599731527140827530319488791822858978924780015280035310521766457660381662363459675166288099343838361130665940967928850877954452552005403436587169730515877297387774041696625714088910160966686976352250237188765370786055553236020704945964404004577531357576565107610684603955726197582253686411381871520005412537060114403951740688011605681233186481569161991920354077827812176666950510226500521720520469387009627382085749910481677989034236154462513159644551504513525508614268492165297534777956118363272320828495465015734808069866823697938666550506233479919235237378935603448169915183235443
14: 100483353306517857188816511171973264968130481955993490961776578914384855009465596512878627978186320098524674810822809215084298821790532480217571435837318997038501027166944291436298311859998927368878478765662052261013905379683606908563327049366289350227874801320137528476359434996625155321924896471487253609774383161294073700386567438895729619959183688827019175395384990049660760826706275656247200320644562229907983316938796200727194177710641698165578469600709422183645673081099011178658794923207340118316226811044120124994280172667435132674250477913878334229469634774955766654959747171269329356217729819952093850230832136940392143299736102334976183356619572749168857678782222255344301700168226608019630704240193738779198063738629831841413772846575231497629810592678428725195220732911880790353530776313807267315574488856933933931968726196972550157616749777588888821303729634383570842953721086839502335017753789603211887639264756326943906234925564059713122739441052488376985825209930025027331642643833862623818612641648534007690784009230583997364206027891426162271405399576520661523570494921380174573570295575834537952976231451138917903119690734728050868143651943079046629073247009723903287946523072583428647088990713577505274669321894108556505593299658881909461644436220683735665670039545950199079805499092674406353548516096407916275052371510047476698658893306349068133879014809524920709542592832744670134019181012820484031829100985336532444887396195766078330294774788615792775829183741076029977456631131003360810557200089618493958319779112283680033864350359591347851857639767660909655544622503481811302270128415655545885368248621757558781407774929247336942808205264958129961178967782261436710020914320953492879039247990865098954170193648898076402861312803632817456574773061811978648089614340109760702469211985641224691799075765885167117855362986656144090527289697873066081524676142089795828969028242126025160985084779781007974719610529121366009147473928798323429514961662955075830495059188425232901129844306717176754536658533793214326255403412914373598713551532524170357661947859352181097102731800860434424406585016086605044703266455861041380556886689319004123095655013285849524741495205262970148746426581276319938997140587845485798731493239638046736464142096404810367841352036464369335995230683471276720095626585363049720580305501778636182605592068492151793190258602236893550140479021220581841241476297575889705144565984983772835663470728331437295945770147420128139970898197153180098987682528952187399111614545313650329728193759220800741639763444502297436225484681500013482802572032911312979385547883726365017125898034265710900263014307543995711388447583272341504352098242603013317289071851486202200363353430637400418445403028209289752937101610106546407815385279051077386957963745649023423516876644029840971378691516442745761797057396994687382618710236478541855961623090443801434726418529440871490091117324165342131670988126442133481305788646667033011070351616554711007362680081909808994105138595194669575127185645557552945017168697977343707144183186705714691228418618276386168995938283316172058534438295911377445943568762495111242585896098376432273844229629284777619272064792008892485171141118486114024760197688360378085790695965894817048250719620713759873671293320363983916413298621510321025850259140267373664767105414000002388170807
15: 10096904291722493183368071064267380357661660106693410869782248738635339952029780296539828646172395134010176258872559248732741423552501907091337488535022650906084259275771532963008605081632727310004012388176378536060181935481315268687099524445976260304963174491384169963045142817764845502919067852341670367757214257530633293876394038000350905620840512848346819593805771248299327648920495911888951338828154665350353011028755722053225038368211236471204894130005662338828040087277653058053926026954188748978276428965217873579228638399408512216051253190389034963502534563472810420786777664075947493242192178950439356302457015948704092615392563507116646622139031277627186004366940766141012052387764963550498137526380034475497296039349645231313666622023168074000757905961415842342549436827136456191636706102191216058665157997484620186504093031595354885464177047583044817527035079867175693262594053326482246251372100971181835929117940968577571250416834584873665407254954117674557725158296520696253051564213291342016830516195717769009307399800985739314707922476435511042184118717157710123856432818413241079127700236873849278099459856806348919726613157276845134234932007694512914360885347631604498444654808443385936829467322014251107608292907841706266154583649605962409356906673289214039345980157983585238598611007015744123201308500000501171750479205303582207819895099792053754750437003972197944606653029649026511175714325665022972458270451004669272442201984239750747468526034925512545591753011926422349450964423576514073138580199215901274311120011401651594856947935270421689304827295107046206967840957322813332397883867061874677422607993141403436835194178479678002082797785957214499969042437649907039865138475341601851262738461348829498716689032746766421448268807692569878289178989757874505465513706845654082199878640106345757795320020739808531463815126727793408754933994363877756899864984281822553007221098602810615408658488405255740618942035792348576150930466937442754907072240355711448059483670791970963065005273062169924072707136909529672907160105055146511078451274809649030962702634933950427417208754579558886670435513091693673392184012357060290800383391444894054478864880104489516105493654428700350038712306497215399390236421973359744231122582759112860245414994943705887755550168313104764831522917085274446816071187952611343217412489624486276718615486137440593087587611396073446784461983318011057978917824445958877834279858529200202638788438701918355676112013825796803683126156843171950302720509023656389038392904612771500795961428815515700691617938343841438201393483006625614378303192786900137915585090133838299336587186981703609917848314020827402418570324364874947405687083727868993183779937556273574979260142267138459345033733513139351742945236547818177589597395538573007069591004145636009266460791802852586248255385289853281955169539287181071240815317693402096387634696936821000809631189985664604670044343502290633727054957569135476042643752035180934112239281974650350606386279562906729624417142767675201654289420896239230816419019207223473210929276206272092462056393663617978292734035101190436048576301803958886273461936172885771511862036063913756041537697347875482651037641523871879511678343487920223572132145739383709173152270680681310792907045630147132642987006838913096888964072928407230377138093587963274543641998748031680910300484752483355961271051871764670801481617005498624008434455328965073448480620868102535798012683148073884828324180309706818271859159551486830624586719405678169003856743183359837325497215633938263574447227327183271417291639794183966954289906892687109652179007215463563426176830359892183207233285822949660507077627537452834236906264132679889387996620400887660540962057531356190936101639054478093742499726068975793037082183383865686389498095746349939423534144214424590382440964976484867660771427325735849308944235845015356241354445696546089110157687163547154187467782703339375797651594636517829331851603968540007770827383674978837195667966783942598590005707606899598870358218737372718556947211584091628920829232578301363561094654677362755304340099041557393126374570806664174774672252295969797311898222174146620044760522846344262741406020752321947103535566408000012063814621832503287764621196638959476702017397368768611288471914511970208911319812356033065360580161537672606063147955100825583445007228467438964318530588833314227952807420669509481593752391013652385527265940130738577518623923144732574439124910418367782835256447209415920224852739207102376107549910900016609384699171269913834437302619696395967407403281737973927596729463096846440722701084830141077051693427101822933034765921597611642383174592217106235280063364807994845967928868775308917858901963126456181289228987259157357205165107173015949882380826616387118049560139377785643404568749158677579677208043068040426770373946180960339686720961911527699043135729279627875429387003955052493364045280876757418765025033413409695324102028154397073950951401567130147958372561569250050115315916847340453713208876117379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16: (13341 digits)
17: (26681 digits)
18: (53361 digits)
19: (106721 digits)
20: (213441 digits)
21: (426881 digits)
22: (853761 digits)
23: (1707522 digits)
24: (3415043 digits)
25: (6830085 digits)
26: (13660169 digits)
27: (27320338 digits)
28: (54640675 digits)
29: (109281349 digits)

As you can see, these numbers grow quite rapidly; the computation time also increases in the same proportion as the result length. It took me half a minute to compute a(23), and several hours for a(29).

Answer 21

JavaScript (ES2016), 25 bytes

f=x=>x--?f(x)**2-f(x)+1:2

Uses the zero-indexed sequence.

Here's an example:

f=x=>x--?f(x)**2-f(x)+1:2

const output = document.getElementById('output');

for(let i = 0; i < 10; i++)
  output.textContent += 'f(' + i + ') = ' + f(i) + '\n';

<pre id="output"></pre>

Answer 22

Groovy, 26 bytes

This answer was basically stolen from @Geobits.

a={n->n--?a(n)*~-a(n)+1:2}

Took that answer and, using groovy shortcuts, optimized it further.

Answer 23

Common Lisp, 53 bytes

(defun f(n)(do((x 2(1+(* x(1- x)))))((<(decf n)0)x)))

The result is computed through the formula a(n+1) = a(n) * (a(n) - 1) + 1, starting from 2 and iterated n times.

Answer 24

Husk, ¹¹ 7 bytes

!¡o→Π;2

Try it online!

1-indexed.

-4 bytes from Leo.

Answer 25

AWK, 32 bytes

{for(n=2;$0>i++;n=n*n-n+1);}$1=n

Try it online!

Answer 26

Vyxal m, 5 bytes

λvxΠ›

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Jelly port.

Answer 27

Thunno 2, 7 bytes

2${D⁻×⁺

Attempt This Online!

Port of Emigna's 05AB1E answer.

Explanation

2${D⁻×⁺  # Implicit input
2        # Start with 2
 ${      # Input number of times:
   D⁻×   #  Multiply by x-1
      ⁺  #  And increment
         # Implicit output

Answer 28

PHP 5.6+ (46 bytes)

function f($n){return--$n?f($n)**2-f($n)+1:2;}

Answer 29

Japt -g, 6 bytes

Takes input as a singleton integer array, 1-indexed.

ÇÆiU×Ä

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Japt -h, 6 bytes

Takes input as an integer, 1-indexed.

ÆßX ×Ä

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Original w/o flag, 9 8 bytes

Takes input as an integer, 0-indexed.

@ÒZ×}gNÅ

Try it

Answer 30

Nekomata, 7 bytes

2ᶦ{:←*→

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Takes no input, and outputs all terms of the Sylvester's sequence.

2ᶦ{:←*→
2           Start with 2
 ᶦ{         Infinite loop:
   :            Duplicate
    ←           Decrement
     *          Multiply
      →         Increment