Create \$n\$ sublists with the powers of two (1, 2, 4, 8, 16...)

Question

Challenge:

Given the input number n. It should give me nested sublists of n layers with the power of two numbers for each level. Each power of two value will be in separate sublists.

Notes:

• n will always be greater than 0

• I am using the example output with Python Lists. You can use any type of sequence in your own language.

• Your output must be one-indexed, add one to n if your output is zero-indexed.

• Your output sequence must be nested.

Test cases:

n = 1: [1]
n = 2: [1, [2]]
n = 3: [1, [2, [4]]]
n = 4: [1, [2, [4, [8]]]]
n = 5: [1, [2, [4, [8, [16]]]]]
n = 6: [1, [2, [4, [8, [16, [32]]]]]]
n = 7: [1, [2, [4, [8, [16, [32, [64]]]]]]]

This is code-golf, so the shortest code in bytes wins!

_{The power of twos are these values 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048..., each values is double of the previous value.}

Answer 1

Factor + math.polynomials, 47 bytes

[ 2 powers reverse 1 cut [ swap 2array ] each ]

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        ! 4
2       ! 4 2
powers  ! { 1 2 4 8 }
reverse ! { 8 4 2 1 }
1       ! { 8 4 2 1 } 1
cut     ! { 8 } { 4 2 1 }
        ! { 8 } 4              <<first iteration of each>>
swap    ! 4 { 8 }
2array  ! { 4 { 8 } }
        ! { 4 { 8 } } 2        <<second iteration>>
swap    ! 2 { 4 { 8 } }
2array  ! { 2 { 4 { 8 } } }
        ! { 2 { 4 { 8 } } } 1  <<third>>
swap    ! 1 { 2 { 4 { 8 } } }
2array  ! { 1 { 2 { 4 { 8 } } } }

Answer 2

><>, 47 bytes

1i:?v~~l?^;
/$-1/
/on$o"[,":
\2*$:}10./"]"o~60.

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Generates trailing commas at the end of lists, some languages allow that so that should be OK. Takes input as a char code.

Uses the length of the stack to keep track of how many ] to generate at the end.

Answer 3

Python 3, 44 bytes

e=lambda n,i=1:[i,e(n-1, i*2)]if n>0 else[i]

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Answer 4

Vyxal, 9 6 bytes

(d1$"ꜝ

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Uses the fact that stack languages can have their input placed on the stack before execution

Proof the meta proposal was +6 at the time of posting

Explained

A port of Jelly

(d1$"ꜝ
(      # repeat input times
 d     # double
  1$"  # [1, that]
     ꜝ #  keep only truthy items

Answer 5

R, 44 bytes

f=\(n,k=1,`+`=list)`if`(n-1,k+f(n-1,k*2),+k)

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Answer 6

05AB1E, 7 bytes

F·Xs‚ZK

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Port of lyxal's Vyxal answer.

• -1 thanks to Kevin Cruijssen

Explanations:

F·Xs‚ZK   # Implicit input (n)
F         # for i in range(a):
 ·        #  Double
  Xs‚     #  Get [1, that] (X defaults to 1)
     ZK   #  Push the list without the maximum

Previous 8 byte answer:

L<o`¸¹G‚   # Implicit input (n)
L<         # range(0, n)
  o        # 2 to the power of each
   `¸      # Dump onto stack, putting the last one in a list
     ¹G    # n-1 times:
       ‚   #  Pair

Previous 13 byte answer:

<Do¸sE¹<N-o‚R   # Implicit input (n)
<               # Reduce n by 1
 Do¸            # Duplicate and push [2**(n-1)] to the stack
    sE          # Swap and loop through range(0, n-1):
      ¹<N-      #  Subtract from n-1
          o     #  Raise 2 to the power of this number
           ‚R   #  Pair and reverse

Answer 7

JavaScript (Node.js), 31 bytes

f=(x,i=1)=>--x?[i,f(x,i*2)]:[i]

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Answer 8

MATL, 12 bytes

:qWP"@XhP]&D

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:       % Implicit input, n. Range [1 2 ... n]
q       % Subtract 1, element-wise
W       % Powers of 2, element-wise
P       % Flip. Gives [2^(n-1) 2^(n-2) ··· 1]
"       % For each number in that vector
@       % Push current number
  Xh    %   Concatenate all stack contents into a cell array
  P     %   Flip
]       % End
&D      % String representation. Implicit display

Answer 9

Pyth, 20 bytes

L+[^2b)?qtQbY[yhb)y0

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L                      # Function y with input as b
 +                     # Append
  [^2b)                # List with 2^b as only element
       ?               # Ternary operator
        qtQb           # If b is equal to input - 1
            Y          #  empty list (when condition is true)
             [yhb)     # Call function y with input b+1 and put inside a list (when condition is false)
                  y0   # Call function y with input 0

Answer 10

Pip, 28 bytes

FiR,a{YlAEyPE EiUi=a?Y Hy0}y

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FiR,a{YlAEyPE EiUi=a?Y Hy0}y
FiR,a{                    }    Loop through [a, 0]
      YlAEyPE Ei               Set y (initially "") to y + 2**i wrapped in a list
                Ui=a?Y Hy0     Remove the empty string if it is the first iteration

```

Answer 11

Jelly, 7 bytes

Ḥ1,¹ƇƲ¡

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-2 bytes thanks to caird coinheringaahing (use STDIN to avoid needing the leading 0, and a shorter way of filtering the 0)

Ḥ1,¹ƇƲ¡    Main Link (input in STDIN, so argument starts at 0)
      ¡    repeat N times
Ḥ          double the current list
 1,        pair with 1
   ¹Ƈ      filter by identity; remove falsy elements (filter out the 0 in the first step)

Answer 12

Knight (v2), 35 bytes

;=l,=c/^2=pP2;W=p-EpT=l+,=c/c 2,lDl

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Looks golfable.

Answer 13

Ruby, 36 34 bytes

->n{*r=k=2**n;n.times{r=k/=2,r};r}

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Answer 14

Python 3, 68 bytes

def f(n):
	for i in range(n):l=i and[l[0]//2,l]or[2**n//2]
	return l

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Answer 15

Charcoal, 14 bytes

ＦＮ≔Φ⟦¹⊗υ⟧κυ⭆¹υ

Try it online! Link is to verbose version of code. Explanation:

ＦＮ

Repeat n times...

≔Φ⟦¹⊗υ⟧κυ

... double the predefined empty list and prepend a 1 (but on the first pass filter out the list as it is empty).

⭆¹υ

Pretty-print the final list.

Answer 16

Python 3, 48 42 40 bytes

f=lambda n,c=1:n>1and[c,f(n-1,c+c)]or[c]

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-6 bytes thanks to l4m2

-2 bytes thanks to The Thonnu

Answer 17

Retina, 36 bytes

"$&"{`\d+
$.(*2*
.+
[1, $&]
, \d+]
]

Try it online! Link includes test cases (because fortunately I was able to use $& instead of $+). Explanation:

"$&"{`

Repeat the program n times (because n is the input).

\d+
$.(*2*

Double all of the integers.

.+
[1, $&]

Wrap the list with 1 in a sublist.

, \d+]
]

Remove the original input.

Answer 18

sclin, 19 bytes

[1]"2*1rev ,";1- *#

Try it here! Takes the argument from the next line. If outputting as an infinite sequence were allowed, then something like 1,,"2*1rev ,"itr would be 16 bytes.

For testing purposes:

; n>o
1,,"2*1rev ,";1- *#
7

Explanation

Prettified code:

[1] ( 2* 1rev , ) ;1- *#

• [1] starting with 1-length array of 1
• (...) ;1- *# repeat (next line) - 1 times...
  • 2* 1rev , vectorized-multiply by 2 and prepend 1

Answer 19

Raku, 23 bytes

[1],{[1,2 «*«$_]}...*

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This is an expression for the infinite sequence of arrays. The magic is in the «*« operator, which multiplies each element of an arbitrarily-deeply nested structure by a number.

Answer 20

Pip -p, 12 bytes

LaYFI[1y*2]y

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Explanation

Same idea as hyper-neutrino's Jelly answer:

LaYFI[1y*2]y
              a is command-line argument; y is "" (implicit)
La            Loop a times:
       y*2      Multiply y by 2 (-> 0 if it's "", element-wise if it's a list)
     [1   ]     Put 1 and that value in a list
   FI           Filter, removing falsey values (in this case, 0)
  Y             Yank, assigning the result back to y
           y  After the loop, autoprint the final value of y

Answer 21

Pip -p, 18 14 bytes

FI[EiUi<a&REa]

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-4 bytes thanks to @DLosc

Recursively builds the nested lists. FI is used to filter out the 0 in the last list, otherwise [1;[2;[4;0]]] would be output.

Answer 22

K (ngn/k), 17 bytes

{(x-1)(1,,2*)/,1}

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Explanation:

{(x-1)(1,,2*)/,1}
              ,1  start with list one
 (x-1)       /    do n-1 times
      (1,,2*)     1 joined with double the current value enlisted

Answer 23

MathGolf, 6 bytes

Æ∞1\αç

Port of @lyxal's Vyxal answer.

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Explanation:

Æ       # Loop the (implicit) input amount of times,
        # using the following five characters as inner code-block:
 ∞      #  Double all current values (the stack contains a 0 by default)
  1\α   #  Pair it with a leading 1
     ç  #  Falsey filter to remove the 0
        # (after the loop, the entire stack is output implicitly as result)

Answer 24

Julia 1.0, 21 bytes

!n=[n<2||[1,2*!~-n];]

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using √ instead of ! would save a character, since a√b is parsed as a*√b (which doesn't work for !). But of course the byte count would be higher.

Answer 25

FunStack alpha, 40 bytes

Pair 1 Double over iterate Wrap 1 At Dec

Try it at Replit: pass the input number as a command-line argument and enter the program on stdin.

Explanation

First, we generate the infinite sequence of such nested lists:

Pair 1

Given x, turn it into [1, x].

Double

Multiply by 2 (applies itemwise over lists).

over

Given two arity-1 functions, this modifier works the same as compose but is 3 bytes shorter. The composed function is "Multiply the argument by 2 and pair 1 with the result."

iterate

Repeatedly apply this function and return the infinite list of results...

Wrap 1

... starting at [1].

The resulting infinite list is a value at the left side of the program, so it gets pushed onto the argument list. Then:

At

Get the nth element, where n is...

Dec

... the first program argument, decremented (since indexing is 0-based).

Answer 26

CJam, 14 bytes

{,W%{2\#]W%}%}

Anonymous code block that pops a number from the stack and pushes the nested array.

The header reads the input. The footer executes the block and prints the string representation of the array.

Port of my MATL answer.

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Code explanation

{,W%{2\#]W%}%}

{            }   e# define code block
 ,               e#   range (0-based)
  W%             e#   reverse array
    {      }%    e#   map this code block over the array
     2\#         e#     exponential with case 2 
        ]        e#     pack all stack contents into an array
         W%      e#     reverse array

Answer 27

Mathematica 39 bytes

With n=5

s=Nothing;Do[s={2^--i,s},{i,n,1,-1}];s

{1, {2, {4, {8, {16}}}}}

Answer 28

awk solution - different solutions for mawk-1/2 and gawk/nawk :

jot 16 | 

mawk 'function __(_){return $_=--_?_+=_=__(_):!_}__(NF=$_)' OFS=,

nawk
gawk 'func __(_){return $++_=--_?__(_)/_*(_+_):!_}__(NF=$-_)' OFS=,

 * "function" is normally preferred, but this is Pebble Beach…

1
1,2
1,2,4
1,2,4,8
1,2,4,8,16
1,2,4,8,16,32
1,2,4,8,16,32,64
1,2,4,8,16,32,64,128
1,2,4,8,16,32,64,128,256
1,2,4,8,16,32,64,128,256,512
1,2,4,8,16,32,64,128,256,512,1024
1,2,4,8,16,32,64,128,256,512,1024,2048
1,2,4,8,16,32,64,128,256,512,1024,2048,4096
1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192
1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384
1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768
1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536

Different solutions needed stemming from their different order of precedence of something not clearly specified in POSIX -

• mawks go strictly left-to-right, even for assignments,

  — so $_ = ... is equivalent to $(func-input-val) = ...,

• while gawk/nawk handles all of RHS first, with LHS taking on final value of _

To make nesting sublists out of that :

 for __ in $(jot 7); do 
  
    echo " $__ :: $( echo "$__"  | 
      
       mawk 'function __(_){ORS="]"ORS;return $_=\
             --_?_+=_=__(_):!_}$!__(NF=$(OFS=",["))="["$_' 

    )"
 done

 1 :: [1]
 2 :: [1,[2]]
 3 :: [1,[2,[4]]]
 4 :: [1,[2,[4,[8]]]]
 5 :: [1,[2,[4,[8,[16]]]]]
 6 :: [1,[2,[4,[8,[16,[32]]]]]]
 7 :: [1,[2,[4,[8,[16,[32,[64]]]]]]]

Answer 29

Scala, 70 bytes

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def e(n:Int,i:Int=1):List[Any]={if(n>0)List(i,e(n-1,i*2))else List(i)}

Answer 30

Lua, 59 bytes

load"a={1}b=a for i=2,...do b[2]={2^i/2}b=b[2]end return a"

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Ungolfed version:

function f(n)
    a={1}b=a
    for i=2,n do
        b[2]={2^i/2}
        b=b[2]
    end
    return a
end