# Generate the Abacaba sequence

This challenge is about printing the abacaba sequence of a specific depth.

Here is a diagram of the first 5 sequences (a(N) is the abacaba sequence of depth N, upper/lowercase is just to show the pattern, this is not needed in the output of your program):

a(0) = A
a(1) = aBa
a(2) = abaCaba
...


As you can probably tell, the n'th abacaba sequence is the last one with the n'th letter and itself again added to it. (a(n) = a(n - 1) + letter(n) + a(n - 1))

Your task is to make a program or function that takes an integer and prints the abacaba sequence of that depth. The output has to be correct at least for values up to and including 15.

• Wouldn't the sequence be undefined after 𝑎₂₅? Jan 9, 2016 at 13:04
• @nicael I know, I was just wondering how 𝑎(∞) would be defined. Jan 9, 2016 at 13:29
• Also known as the ruler sequence (but with letters instead of numbers), for something more easily Google-able. Jan 10, 2016 at 6:00
• For what it's worth, any valid solution to this problem is also the solution to the Towers of Hanoi puzzle for N disks. Apr 2, 2019 at 11:59
• Can we use 1-based indexing instead of 0-based indexing? Apr 3, 2019 at 17:21

# Pyth, 11 bytes

u++GHG<GhQk


Simple reduction.

• @Loovjo Oh. Makes no sense, 0 should be the empty sequence IMO, but I'll conform to the question...
– orlp
Jan 9, 2016 at 12:52
• Yeah, simple. goes and bangs head on wall Feb 13, 2016 at 20:07
• @JAtkin Open up Pyth's rev-doc.txt next to this answer, and it should readily show itself to be simple.
– orlp
Feb 13, 2016 at 20:19
• Hehehe, not what I meant (I don't know pyth, so....) Feb 13, 2016 at 20:22

## Python, 44 bytes

f=lambda n:"a"[n:]or f(n-1)+chr(97+n)+f(n-1)


Looks suspiciously might-be-golfable.

a 0="a"
a n=a(n-1)++['a'..]!!n:a(n-1)


Usage example: a 3 -> "abacabadabacaba".

Edit: @Angs found two bytes to save. Thanks!

• Wouldn't a n=a(n-1)++[97+n]++a(n-1) work? Can't test right now. Jan 9, 2016 at 18:36
• @Seeq: no, [97+n] is a list of Integer and a(n-1) is a list of Char (aka String). You cannot concatenate lists with different types. toEnum makes a Char out of the Integer.
– nimi
Jan 9, 2016 at 18:57
• Ah, I always thought Char was just a specialized integer in Haskell. Jan 9, 2016 at 23:47
• ['a'..]!!n is 2 bytes shorter than toEnum(97+n)
– Angs
Oct 6, 2016 at 18:11
• @Angs: Good catch! Thanks!
– nimi
Oct 6, 2016 at 22:29

# Pyth, 14 13 bytes

Thanks to Jakube for saving a byte!

VhQ=+k+@GNk;k


A solution with 14 bytes: VhQ=ks[k@GNk;k.

Explanation:

VhQ=+k+@GNk;k

# Implicit: k = empty string
VhQ            # For N in range input + 1
=           # Assign k
+@GNk    # Position N at alphabet + k
+k         # k + above
;   # End loop
k  # Print k


Try it here!

• Shouldn't "N in range" be on the V line? hQ is just eval(input) + 1 Jan 9, 2016 at 12:58
• @Loovjo Yeah, that's better and less confusing :) Jan 9, 2016 at 13:00
• You can shorten =k to =. Pyth will automatically assign the result to k, since k is the first variable in the expression +k+@GNk. Jan 9, 2016 at 14:00
• @Jakube Thank you very much! :) Jan 9, 2016 at 14:10
• I have a different answer for this challenge. It won't beat this solution, but it does illustrate a technique for giving the first n characters of the sequence: Vt^2Q=+k@Gx_.BhN1)k (In this instance, it's set to give the first 2^Q-1 characters as the challenge requires, but you can see how to change that.) Jan 9, 2016 at 22:12

# Brainfuck, 157 bytes

,+>-[>++<-----]>----->>+<<<<[->>[[->>[>>>]<+<+<[<<<]>>[>>>]<]>>[>>>]<[-<<[<<<]>>[>>>]<+>>[>>>]<]+>+<<<[<<<]>>[>>>]+[>>>]<]<<<+>>[<-<<]<]>>>>[>>>]<<<<<<[<<.<]


Input is given in binary.

The basic idea is to repeatedly duplicate the current sequence (starting with "a") and to increment the last element after each iteration:

1. a → aa → ab

2. ab → abab → abac

3. abac → abacabac → abacabac

4. ...

When all of this has been done the specified amount of times, the result gets printed excluding the last element.

## In-depth explanation

The memory is arranged in the following way:

.---------.-.-----.----.---.-----.----.---.---
|Countdown|0|Value|Copy|End|Value|Copy|End|...
'---------'-'-----'----'---'-----'----'---'---

|--Element 1---|--Element 2---|


Countdown holds the number of copy cycles that are yet to be executed. The ABACABA sequence is stored in adjecent blocks, each made up of 3 cells. Value holds the character of the element (i.e. "A","B","C"...). The Copy flag indicates whether or not the corresponding element needs to be copied within the current copying cycle (0=copy, 1=don't). The End flag is set to 0 for the last element while it is being copied (it's 1 in all other cases).

Now to the actual (slightly ungolfed) program:

,                       read Countdown from input
+                       add 1 to avoid off-by-one error
>-[>++<-----]>-----     initialize value cell of first element to 97 ("a")
>>+                     set End flag of first element to 1
<<<<                    move to Countdown
[                       loop until Countdown hits 0 (main loop)
-                   decrement Countdown
>>                  move to Value cell of first element
[                   copying loop
[               duplication sub-loop
-           decrement Value cell of the element to copy
>>          move to End flag
[>>>]       move to End flag of the last element
<+<+        increment Copy and Value cell of last element (Copy cell is temporarily abused)
<           move to End flag of second to last element
[<<<]>>     move back to Copy cell of first element
[>>>]<      move to Value cell of the first element where the Copy flag is 0
]
>>[>>>]<        move to (abused) Copy flag of the last element
[               "copy back" sub-loop
-           decrement Copy flag
<<          move to End flag of second to last element
[<<<]>>     move back to Copy cell of first element
[>>>]<      move to Value cell of the first element where the Copy flag is 0
+           increment Value cell
>>[>>>]<    move back to Copy flag of the last element
]
+>+             set Copy and End flag to 1
<<<             move to End flag of second to last element
[<<<]>>         move back to Copy cell of first element
[>>>]<          move to Value cell of the first element where the Copy flag is 0
>+<             set Copy flag to 1
>[>>>]<         move to Value cell of the next element to copy
]                   loop ends three cells behind the last "valid" Value cell
<<<+                increment Value cell of last element
>>                  move to End flag
[<-<<]              reset all Copy flag
<                   move to Countdown
]
>>>>                    move to End flag of first element
[>>>]<<<                move to End flag of last element
<<<                     skip the last element
[<<.<]                  output Value cells (in reverse order, but that doesn't matter)

• Welcome to the site! I'd be interested in a more detailed breakdown! Apr 3, 2019 at 14:15
• @SriotchilismO'Zaic Thanks for your reply :) I have now added a detailed explanation. Apr 3, 2019 at 20:46

## Retina, 37 32 bytes

$aa (T_ll.$
)1(a.*)
$1$1
z



The trailing linefeed is significant. Input is taken in unary.

Try it online!

• It does not work. Mar 31, 2016 at 4:47
• @KennyLau yes, because Retina changed since I posted this answer. If you check out the release that was most recent when this was posted directly from GitHub, it will work with that. Mar 31, 2016 at 5:25

tail.(iterate((:"a").succ=<<)"_a"!!)


Try it online!

This uses a different recursive method from most of the other answers. To get the next string in the sequence, we don't join two copies in the previous string with a new letter in between, but instead increment every letter and intersperse a's.

aba -> bcb -> abacaba


# 05AB1E, 12 bytes (non-competitive)

Code:

'aIGDN>.bsJl


I'll be damned. I fixed a lot of bugs thanks to this challenge haha.

Explanation:

'aIGDN>.bsJl

'a             # Push the character 'a'
I            # User input
G           # For N in range(1, input)
D          # Duplicate the stack
N         # Push N
>        # Increment
.b      # Convert to alphabetic character (1 = A, 2 = B, etc.)
s     # Swap the last two elements
J    # push ''.join(stack)
l   # Convert to lowercase
# Implicit: print the last item of the stack

• Why is it non-competitive? Jan 9, 2016 at 13:31
• @Loovjo I fixed the bugs after the challenge was posted, therefore it's non-competitive :( Jan 9, 2016 at 13:32

# JavaScript (ES6), 43 42 bytes

a=n=>n?a(--n)+(n+11).toString(36)+a(n):"a"


A byte saved thanks to @Neil!

Yet another simple recursive solution...

• (n+11).toString(36) saves you 1 byte, and works for up to a(25)!
– Neil
Jan 9, 2016 at 18:08
• @Neil Implemented. Thanks! Jan 10, 2016 at 2:24

# jq-r, 43 bytes

def f:.-1|[[97]][.+1]//f+[.+98]+f;f|implode


Try it online!

With the capitalization pattern from the example outputs, 58 bytes:

def f:[[65]][.]//([.-1|f[]%32+96,.+66]|.+.)[:-1];f|implode


Try it online!

def f:    ...       ;  define a filter named f
[[65]][.]        base case, if the argument . is 0, return [65]
//               otherwise
.-1|f         call the filter recursively
[]%32+96      convert each codepoint to lower case
,.+66        append .+66 (. is now the filter argument -1)
[ ... ]       collect all codepoints in an array
|.+.          and repeat that array twice
[:-1]         remove the last integer
f|implode              call the filter on the input and convert the result to a string


'aqi{'b+1$++}/  Online demo # Ruby (1.9 and up), 38 bytes ?a is a golfier way to write "a" but looks weird when mixed with ternary ?: a=->n{n<1??a:a[n-1]+(97+n).chr+a[n-1]}  # R, 48 bytes f=function(n)if(n)paste0(a<-f(n-1),letters[n],a)  Try it online! Simple recursion. • Uh, what is paste0??? Apr 23, 2019 at 20:34 • @Xi'an paste0 is equivalent to paste with sep="", so you avoid the spaces between letters that paste would add by default. Apr 24, 2019 at 10:48 # jq, 51 bytes [range(.)+97|[.]|implode]|reduce.[]as$i("a";.+$i+.)  Try it online! My life has improved significantly since I found reduce in this language. -16 bytes from ovs. # Labyrinth, 31 bytes _-)"(;; (. ? {_ @ +}989 1_  Try it online! I feel like this can be rearranged to be golfier, but a better layout eludes me. I also have a cleaner 1-indexed version which has a higher ratio of walls. This uses xnor's method of repeatedly incrementing the string and interspersing with as. # C#, 59 bytes string a(int n){return n<1?"a":a(n-1)+(char)(97+n)+a(n-1);}  Just another C# solution... # Perl, 33 bytes map$\.=chr(97+$_).$\,0..pop;print


No real need for un-golfing. Builds the string up by iteratively appending the next character in sequence plus the reverse of the string so far, using the ASCII value of 'a' as its starting point. Uses $\ to save a few strokes, but that's about as tricky as it gets. Works for a(0) through a(25) and even beyond. Although you get into extended ASCII after a(29), you'll run out of memory long before you run out of character codes: a(25) is ~64MiB. a(29) is ~1GiB. To store the result of a(255) (untested!), one would need 2^256 - 1 = 1.15x10^77 bytes, or roughly 1.15x10^65 1-terabyte drives. • We need those atom-shudder yottabyte drives, now! Mar 10, 2016 at 20:10 # MATL, 14 bytes 0i:"t@whh]97+c  This uses version 8.0.0 of the language/compiler, which is earlier than the challenge. ### Example >> matl > 0i:"t@whh]97+c > > 3 abacabadabacaba  ### Explanation The secuence is created first with numbers 0, 1, 2, ... These are converted to letters 'a', 'b', 'c' at the end. 0 % initiallize: a(0) i: % input "N" and create vector [1, 2, ... N] " % for each element of that vector t % duplicate current sequence @ % push new value of the sequence whh % build new sequence from two copies of old sequence and new value ] % end for 97+c % convert 0, 1, 2, ... to 'a', 'b', 'c'. Implicitly print  ### Edit Try it online! # Java 7, 158 bytes class B{public static void main(String[]a){a('a',Byte.valueOf(a[0]));}static void a(char a,int c){if(c>=0){a(a,c-1);System.out.print((char)(a+c));a(a,c-1);}}}  I like to lurk around PPCG and I would enjoy being able to vote/comment on other answers. Input is given as program parameters. This follows the same format as many other answers here in that it's a straight forward recursive implementation. I would have commented on the other answer but I don't have the rep to comment yet. It's also slightly different in that the recursive call is done twice rather than building a string and passing it along. • Welcome to PPCG then! I hope you'll do some more than voting and commenting in the future (but don't feel like you have to). :) Apr 11, 2016 at 19:47 # Mathematica, 36 32 bytes ##<>#&~Fold~Alphabet[][[;;#+1]]&  Have you ever watched TWOW 11B? • There is no need for the "", and then you can use infix notation for Fold. Sep 22, 2016 at 17:24 • #1 causes null <>s, and #2 only works for binary functions. Oct 15, 2016 at 15:36 • Did you post this comment on the answer you intended? Because I have no idea what you mean. :) Oct 15, 2016 at 15:39 • *#1 causes StringJoin to join nulls, and #2 only works for binary or associative functions. (x~Fold~y~Fold~z=Fold[x,Fold[y,z]] instead of Fold[x,y,z]) Oct 15, 2016 at 15:42 • Oh you mean "suggestion #1". No it doesn't cause Nulls. Why would it? Oct 15, 2016 at 15:44 # Husk, 12 bytes !¡S+oṠ:o→▲"a  Try it online! Uses 1-based indexing, which I hope is OK. ## Explanation ! ( !!) ¡ iterate( ) S <*> + (++) o ( ) Ṡ join$   .
:                             (:)
o                                    .
→                               succ
▲                                   maximum
"a                                          "a"

(iterate((++)<*>(join$(:).succ.maximum))"a"!!)  # Python, 625446 45 bytes I would like to think that this code can still be golfed down somehow. Edit: Bug fix thanks to Lynn. -1 byte thanks to squid. a=lambda n:n and a(n-1)+chr(97+n)+a(n-1)or'a'  Try it online! • Output should be in all-lowercase. The uppercase in the question is just for clarity about the repetition. Jan 9, 2016 at 12:56 • Whoops. Thanks for the clarification. Jan 9, 2016 at 12:58 • Blargle. Thanks @user81655 Jan 9, 2016 at 13:20 • This is invalid (it never terminates — try it). Even in the base case, the recursive part of the expression is evaluated. – Lynn Apr 2, 2019 at 22:21 • Fixed. Thanks @Lynn! Apr 3, 2019 at 5:29 # Vim, 35 bytes :h<_ jjYZZpqqv|yPyl/<c-r>" xq{Dddl@-@qD  Try it online! ### Explanation The buffer starts with a single line containing the input integer. :h<_ jjYZZp  Yank the lowercase alphabet from the help file. Paste it on a new line below the integer, leaving the cursor on the first character of the second line. qq  Start recording macro q. This will be our "loop." v|y  Using visual mode, select everything from the current character to the beginning of the line, inclusive, and yank it. This leaves the cursor on the first character of the line. P  Paste the yanked text to the left of the cursor. The cursor is now on the last of the pasted characters. yl  Yank that character. /<c-r>" x  Find the next occurrence of the just-yanked character. Delete it. q  Stop recording the macro. Conveniently, this first time through the macro has left the alphabet unchanged. The only effect is that the cursor has moved from the a to the b. {Dddl  Go to the beginning of the buffer. Delete the contents of the first line (the input number). Then delete the (now-empty) first line. Move the cursor one character to the right so as to start on b. @-@q  Execute the macro N times, where N is the number we just deleted. D  Delete the unused remainder of the alphabet. Normally, the @-@q idiom is fraught with peril if the number has a chance of being zero, because 0 is not a valid count in Vim; instead, it is treated as a separate command that move the cursor to the beginning of the line. However, in this particular case, an input of 0 is no problem at all: @-  Move the cursor to the beginning of the line. @q  Execute the macro once. Recall that executing the macro with the cursor on the a leaves the alphabet unchanged and the cursor on the b. D  Delete everything to the end of the line--which leaves only the a, exactly the output we want. # Knight (v2.0-alpha), 37 bytes ;=q+96=n+1P;=x"";W=n-nT=x++xA-q n xOx  Try it online! Expanded ; = q (+ 96 (= n (+ 1 PROMPT))) ; = x "" ; WHILE (= n (- n TRUE)) = x (+ (+ x (ASCII (- q n))) x) : OUTPUT x  # Thunno 2J, 9 bytes Oėıf2c;⁺Ä  Attempt This Online! Port of emanresu A's Vyxal answer. #### Explanation Oėıf2c;⁺Ä # Implicit input O # Push 2 ** input ė # Push [1..that) ı ; # Map: f # Prime factors 2c # Count 2s ⁺Ä # Letter of alphabet # Implicit output  # Vyxal, 61 bitsv2, 7.625 bytes ¤$(nøAȮW∑


Try it Online!

Uses 1-indexing.

## Explained

Generated using Luminespire

¤$(nøAȮW∑ ¤$         # Push an empty string under the input
(        # For each n in the range [1, input]:
nøA     #   Get the nth letter of the alphabet
Ȯ    #   Push a copy of the item under the top of the stack. This leaves the stack as [already generated, new letter, already generated]
W∑  #   Wrap and sum the stack


# Mathematica, 46 bytes

If[#<1,"a",(a=#0[#-1])<>Alphabet[][[#+1]]<>a]&


Simple recursive function. Another solution:

a@0="a";a@n_:=(b=a[n-1])<>Alphabet[][[n+1]]<>b


# K5, 18 bytes

"A"{x,y,x}/c$66+!  Repeatedly apply a function to a carried value ("A") and each element of a sequence. The sequence is the alphabetic characters from B up to some number N (c$66+!). The function joins the left argument on either side of the right argument ({x,y,x}).

In action:

 ("A"{x,y,x}/c\$66+!)'!6
("A"
"ABA"
"ABACABA"

• I think the sequence should be lowercase, but that costs no bytes. Jan 9, 2016 at 18:05

## JavaScript, 65 571 bytes

n=>eval('s="a";for(i=0;i<n;i++)s+=(i+11).toString(36)+s')


Demo:

function a(n){
return eval('s="a";for(i=0;i<n;i++)s+=(i+11).toString(36)+s')
}
alert(a(3))

1 - thanks Neil for saving 8 bytes

• (i+11).toString(36) saves you 6 bytes.
– Neil
Jan 9, 2016 at 18:14
• @Neil Haha, that's a clever hack Jan 9, 2016 at 18:16
• Oh, and if you move the assignment s="a"; to before the for then it becomes the default return value and you can drop the trailing ;s for another 2 byte saving.
– Neil
Jan 9, 2016 at 18:18
• @Neil Nice, didn't know about that. Jan 9, 2016 at 18:19
• I think you can save a byte by incrementing i inline and dropping the increment in the for loop. So... for(i=0;i<n;)s+=(i+++11)... Mar 11, 2016 at 4:46

# Japt, 20 17 bytes

97oU+98 r@X+Yd +X


Test it online!

### How it works

         // Implicit: U = input integer
65oU+66  // Generate a range from 65 to U+66.
r@       // Reduce each item Y and previous value X in this range with this function:
X+Yd     // return X, plus the character with char code Y,
+X       // plus X.

// Implicit: output last expression


## Non-competing version, 14 bytes

97ôU r@X+Yd +X


The ô function is like o, but creates the range [X..X+Y] instead of [X..Y). Test it online!

I much prefer changing the 97 to 94, in which case the output for 5 looks like so:

^_^^_^a^_^^_^b^_^^_^a^_^^_^c^_^^_^a^_^^_^b^_^^_^a^_^^_^