It's a Bit of a Stretch․․․

Question

Input:

We take two inputs:

• An input b with two distinct values: Left and Right.†
• And a positive integer n.

Output:

Based on the Left/Right input, we output either of the following two sequences in the range of 1-n (in the sequences below the first 125 items are displayed):

Left:
1, 6, 7, 56, 57, 62, 63, 960, 961, 966, 967, 1016, 1017, 1022, 1023, 31744, 31745, 31750, 31751, 31800, 31801, 31806, 31807, 32704, 32705, 32710, 32711, 32760, 32761, 32766, 32767, 2064384, 2064385, 2064390, 2064391, 2064440, 2064441, 2064446, 2064447, 2065344, 2065345, 2065350, 2065351, 2065400, 2065401, 2065406, 2065407, 2096128, 2096129, 2096134, 2096135, 2096184, 2096185, 2096190, 2096191, 2097088, 2097089, 2097094, 2097095, 2097144, 2097145, 2097150, 2097151, 266338304, 266338305, 266338310, 266338311, 266338360, 266338361, 266338366, 266338367, 266339264, 266339265, 266339270, 266339271, 266339320, 266339321, 266339326, 266339327, 266370048, 266370049, 266370054, 266370055, 266370104, 266370105, 266370110, 266370111, 266371008, 266371009, 266371014, 266371015, 266371064, 266371065, 266371070, 266371071, 268402688, 268402689, 268402694, 268402695, 268402744, 268402745, 268402750, 268402751, 268403648, 268403649, 268403654, 268403655, 268403704, 268403705, 268403710, 268403711, 268434432, 268434433, 268434438, 268434439, 268434488, 268434489, 268434494, 268434495, 268435392, 268435393, 268435398, 268435399, 268435448, 268435449

Right:
1, 4, 7, 32, 39, 56, 63, 512, 527, 624, 639, 896, 911, 1008, 1023, 16384, 16415, 16864, 16895, 19968, 19999, 20448, 20479, 28672, 28703, 29152, 29183, 32256, 32287, 32736, 32767, 1048576, 1048639, 1050560, 1050623, 1079296, 1079359, 1081280, 1081343, 1277952, 1278015, 1279936, 1279999, 1308672, 1308735, 1310656, 1310719, 1835008, 1835071, 1836992, 1837055, 1865728, 1865791, 1867712, 1867775, 2064384, 2064447, 2066368, 2066431, 2095104, 2095167, 2097088, 2097151, 134217728, 134217855, 134225792, 134225919, 134471680, 134471807, 134479744, 134479871, 138149888, 138150015, 138157952, 138158079, 138403840, 138403967, 138411904, 138412031, 163577856, 163577983, 163585920, 163586047, 163831808, 163831935, 163839872, 163839999, 167510016, 167510143, 167518080, 167518207, 167763968, 167764095, 167772032, 167772159, 234881024, 234881151, 234889088, 234889215, 235134976, 235135103, 235143040, 235143167, 238813184, 238813311, 238821248, 238821375, 239067136, 239067263, 239075200, 239075327, 264241152, 264241279, 264249216, 264249343, 264495104, 264495231, 264503168, 264503295, 268173312, 268173439, 268181376, 268181503, 268427264, 268427391

How are these sequences generated you ask?

A default sequence from 1 through n=10 would be:

As integer:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10

As binary:
1 10 11 100 101 110 111 1000 1001 1010

When we stretch left, the binary will become this:

1, 110, 111, 111000, 111001, 111110, 111111, 1111000000, 1111000001, 1111000110

Why? The last bit is used once; the single-last is used twice; the second-last is used three times; etc.

So `1010` will become (spaces added as clarification): `1111 000 11 0`

And these new left-stretched binary strings are converted back to integers:

1, 6, 7, 56, 57, 62, 63, 960, 961, 966

---

As for stretched right, the first bit is used once; second twice; third three times; etc. Like this:

As binary:
1, 100, 111, 100000, 100111, 111000, 111111, 1000000000, 1000001111, 1001110000

As integer:
1, 4, 7, 32, 39, 56, 63, 512, 527, 624

Challenge rules:

• † You can take any two distinct values, but state which one you use. So it can be 1/0, true/false, null/undefined, "left"/"right", etc.
• n is always larger than 0.
• You should support a maximum output of at least your language's default integer (which is 32-bit for most languages).
• Output format is flexible. Can be printed or returned as array/list. Can be with a space, comma, pipe, and alike as delimiter. Your call. (Again, please state what you've used.)

General rules:

• This is code-golf, so shortest answer in bytes wins.
  Don't let code-golf languages discourage you from posting answers with non-codegolfing languages. Try to come up with an as short as possible answer for 'any' programming language.
• Standard rules apply for your answer, so you are allowed to use STDIN/STDOUT, functions/method with the proper parameters and return-type, full programs. Your call.
• Default Loopholes are forbidden.
• If possible, please add a link with a test for your code.
• Also, please add an explanation if necessary.

Answer 1

Jelly, 9 bytes

BmxJ$mḄð€

Try it online!

-1 for left, 1 for right.

Answer 2

Python 2, 102 96 bytes

lambda d,n:[int(''.join(c*-~i for i,c in enumerate(bin(x+1)[2:][::d]))[::d],2)for x in range(n)]

-1 for left, 1 for right

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Answer 3

05AB1E, 14 13 bytes

Saved 1 byte thanks to Erik the Outgolfer

LbεIiRƶRëƶ}JC

1 for left.
0 (or anything else) for right.

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Explanation

L                # push range [1 ... first_input]
 b               # convert to binary
  ε              # apply to each
   Ii            # if second_input is true
     RƶR         # reverse, multiply each element with its 1-based index and reverse again
        ëƶ       # else, multiply each element with its 1-based index
          }      # end if
           J     # join
            C    # convert to base-10

Answer 4

Japt, 19 18 17 bytes

0 for "left", 1 for "right". (It can actually take any falsey or truthy values in place of those 2.)

õȤËpV©EĪEnFlÃn2

Test it

---

Explanation

Implicit input of integers U & V.

õ

Create an array of integers from 1 to U, inclusive.

È

Pass each through a function.

¤

Convert the current integer to a binary string

Ë           Ã

Map over the string, passing each character through a function, where E is the current index and F is the full string.

p

Repeat the current character

V©  ª

© is logical AND (&&) and ª is logical OR ||, so here we're checking if V is truthy (non-zero) or not.

YÄ

If V is truthy then X gets repeated Y+1 times.

YnZl

If V is falsey then X gets repeated Y subtracted from (n) the length (l) of Z times.

n2

Convert back to a base 10 integer.

Implicitly output resulting array.

Answer 5

Husk, 13 bytes

mȯḋṠṘo?ḣṫ⁰Lḋḣ

That's a lot of dotted letters...

Takes first b (0 for left and 1 for right), then n. Try it online!

Explanation

mȯḋṠṘo?ḣṫ⁰Lḋḣ  Inputs b=1 and n=5 (implicit).
            ḣ  Range to n: [1,2,3,4,5]
mȯ             Map function over the range:
                 Argument: number k=5
           ḋ     Binary digits: [1,0,1]
   ṠṘ            Repeat each digit with respect to the list
     o    L      obtained by applying to the length (3) the function
      ?  ⁰       if b is truthy
       ḣ         then increasing range: [1,2,3]
        ṫ        else decreasing range: [3,2,1].
                 We get [1,0,0,1,1,1].
  ḋ              Convert back to integer: 39
               Final result [1,4,7,32,39], implicitly print.

Answer 6

Gaia, 15 bytes

⟪¤bw¦¤;ċ%׆_b⟫¦

Uses -1 for left and 1 for right.

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Explanation

⟪¤bw¦¤;ċ%׆_b⟫¦  Map this block over the range 1..n, with direction as an extra parameter:
 ¤                Swap, bring current number to the top
  b               List of binary digits
   w¦             Wrap each in a list
     ¤            Bring direction to the top
      ;ċ          Push the range 1..len(binary digts)
        %         Select every direction-th element of it (-1 reverses, 1 does nothing)
         ׆       Element-wise repetition
           _      Flatten
            b     Convert from binary to decimal

Answer 7

Proton, 79 bytes

n=>d=>[int(''.join(b[x]*[l-x,x-1][d]for x:2..(l=len(b=bin(i)))),2)for i:1..n+1]

0 is left, 1 is right.

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Ungolfed

f=n=>d=>                        # Curried function
[                               # Collect the results in a list
 int(                           # Convert from a binary string to an int:
  ''.join(                       # Join together
   b[x]                           # Each character of the binary string of n
   *[l-x,x-1][d]                  # Repeated by its index or its index from the end, depending on d
   for x:2..(l=len(b=bin(i))))    
 ,2)
 for i:1..n+1                   # Do this for everything from 1 to n inclusive
]

Answer 8

C# (.NET Core), 192 187 + 23 bytes

-5 bytes thanks to TheLethalCoder

b=>n=>new int[n].Select((_,a)=>{var g=Convert.ToString(a+1,2);return(long)g.Reverse().SelectMany((x,i)=>Enumerable.Repeat(x,b?i+1:g.Length-i)).Select((x,i)=>x>48?Math.Pow(2,i):0).Sum();})

Byte count also includes:

namespace System.Linq{}

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Input: left is true, right is false

Explanation:

b => n =>                                   // Take two inputs (bool and int)
    new int[n].Select((_, a) => {           // Create new collection the size of n
        var g = Convert.ToString(a + 1, 2); // Take every number in sequence 1..n and convert to base 2 (in a string)
        return (long)g.Reverse()            // Reverse the bits
               .SelectMany((x, i) =>        // Replace every bit with a collection of its repeats, then flatten the result
                   Enumerable.Repeat(x, b ? i + 1 : g.Length - i))
               .Select((x, i) => x > 48 ? Math.Pow(2, i) : 0)
               .Sum();                      // Replace every bit with a corresponding power of 2, then sum
    })

Answer 9

JavaScript (ES6), 113 bytes

Oh, this is just far too long! This is what happens when you spend the day writing "real" JavaScript, kiddies; you forget how to golf properly!

Uses any truthy or falsey values for b, with false being "left" and true being "right".

n=>b=>[...Array(n)].map(_=>eval("0b"+[...s=(++e).toString(2)].map((x,y)=>x.repeat(b?++y:s.length-y)).join``),e=0)

---

Try it

o.innerText=(f=
n=>b=>[...Array(n)].map(_=>eval("0b"+[...s=(++e).toString(2)].map((x,y)=>x.repeat(b?++y:s.length-y)).join``),e=0)
)(i.value=10)(j.value=1);oninput=_=>o.innerText=f(+i.value)(+j.value)

label,input{font-family:sans-serif;font-size:14px;height:20px;line-height:20px;vertical-align:middle}input{margin:0 5px 0 0;width:100px;}

<label for=i>Size: </label><input id=i type=number><label for=j>Direction: </label><input id=j min=0 max=1 type=number><pre id=o>

Answer 10

JavaScript (ES6), 131 bytes

This is significantly longer than Shaggy's answer, but I wanted to try a purely bitwise approach.

Due to the 32-bit limit of JS bitwise operations, this works only for n < 128.

Takes input in currying syntax (n)(r), where r is falsy for left / truthy for right.

n=>r=>[...Array(n)].map((_,n)=>(z=n=>31-Math.clz32(n),g=n=>n&&(x=z(b=n&-n),r?2<<z(n)-x:b*2)-1<<x*(r?2*z(n)+3-x:x+1)/2|g(n^b))(n+1))

Formatted and commented

n => r => [...Array(n)]       // given n and r
  .map((_, n) => (            // for each n in [0 .. n - 1]
    z = n =>                  //   z = helper function returning the
      31 - Math.clz32(n),     //       0-based position of the highest bit set
    g = n =>                  //   g = recursive function:
      n && (                  //     if n is not equal to 0:
        x = z(b = n & -n),    //       b = bitmask of lowest bit set / x = position of b
        r ?                   //       if direction = right:
          2 << z(n) - x       //         use 2 << z(n) - x
        :                     //       else:
          b * 2               //         use b * 2
      ) - 1                   //       get bitmask by subtracting 1
      << x * (                //       left-shift it by x multiplied by:
        r ?                   //         if direction = right:
          2 * z(n) + 3 - x    //           2 * z(n) + 3 - x
        :                     //         else:
          x + 1               //           x + 1
      ) / 2                   //       and divided by 2
      | g(n ^ b)              //     recursive call with n XOR b
    )(n + 1)                  //   initial call to g() with n + 1
  )                           // end of map()

Demo

let f =

n=>r=>[...Array(n)].map((_,n)=>(z=n=>31-Math.clz32(n),g=n=>n&&(x=z(b=n&-n),r?2<<z(n)-x:b*2)-1<<x*(r?2*z(n)+3-x:x+1)/2|g(n^b))(n+1))

console.log(JSON.stringify(f(10)(false)))
console.log(JSON.stringify(f(10)(true)))

Answer 11

Dyalog APL, 23 bytes

{2⊥b/⍨⌽⍣⍺⍳≢b←2⊥⍣¯1⊢⍵}¨⍳

left is 1 right is 0 (passed in as left argument of function)

⍳ is index generator

{...}¨ apply function in braces to each item on the right

b←2⊥⍣¯1⊢⍵ b is ⍵ encoded as binary (using the inverse of decode to get the minimum number of bits required to represent ⍵ in base 2)

⍳≢b generate indexes for vector b (≢b is length of b)

⌽⍣⍺ reverse ⍺ times (used conditionally here for left or right stretch)

b/⍨ b replicated by (replicates the bits as per the (reverse)index)

2⊥ decode from base 2

TryAPL online

Answer 12

Jelly, 11 bytes

B€xJṚ⁹¡$$€Ḅ

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Argument #1: n
Argument #2: 1 for left, 0 for right.

Answer 13

Retina, 111 bytes

\d+
$*
1
$`1¶
+`(1+)\1
${1}0
01
1
.
$.%`$*R$&$.%'$*L
+s`(R?)(\d)(L?)(.*¶\1\3)$
$2$2$4
¶*[RL]

1
01
+`10
011
%`1

Try it online! Takes the number and either L or R as a suffix (or on a separate line). Explanation:

\d+
$*
1
$`1¶

Convert from decimal to unary and count from 1 to n.

+`(1+)\1
${1}0
01
1

Convert from unary to binary.

.
$.%`$*R$&$.%'$*L

Wrap each bit in R and L characters according to its position in the line.

+s`(R?)(\d)(L?)(.*¶\1\3)$
$2$2$4

Replace the relevant R or L characters with the appropriate adjacent digit.

¶*[RL]

1
01
+`10
011
%`1

Remove left-over characters and convert from binary to decimal.

Answer 14

Ruby, 98 bytes

->n,r{t=->a{r ?a:a.reverse};(1..n).map{|k|i=0;t[t[k.to_s(2).chars].map{|d|d*(i+=1)}].join.to_i 2}}

Answer 15

JavaScript (ES6), 130 127 bytes

3 bytes, thanks Kevin

I sure don't know enough ES6 for this site, but I tried! Loop through each number, and loop through each binary representation for that number, repeating each character however many times needed.

d=>n=>{i=0;while(i++<n){b=i.toString(2),s="",k=-1,l=b.length;while(++k<l)s+=b[k].repeat(d?k+1:l-k);console.log(parseInt(s,2))}}

f=d=>n=>{i=0;while(i++<n){b=i.toString(2),s="",k=-1,l=b.length;while(++k<l)s+=b[k].repeat(d?k+1:l-k);console.log(parseInt(s,2))}}
f(1)(10)
f(0)(10)

Answer 16

Java 8, 136 bytes

Lambda (curried) from Boolean to a consumer of Integer. The boolean parameter indicates whether to stretch left (values true, false). Output is printed to standard out, separated by newlines, with a trailing newline.

l->n->{for(int i=0,o,c,d,s=0;i++<n;System.out.println(o)){while(i>>s>0)s++;for(o=c=0;c++<s;)for(d=0;d++<(l?s-c+1:c);o|=i>>s-c&1)o<<=1;}}

Ungolfed lambda

l ->
    n -> {
        for (
            int i = 0, o, c, d, s = 0;
            i++ < n;
            System.out.println(o)
        ) {
            while (i >> s > 0)
                s++;
            for (o = c = 0; c++ < s; )
                for (
                    d = 0;
                    d++ < (l ? s - c + 1 : c);
                    o |= i >> s - c & 1
                )
                    o <<= 1;
        }
    }

Try It Online

Limits

Because they're accumulated in ints, outputs are limited to 31 bits. As a result, inputs are limited to 7 bits, so the maximum input the program supports is 127.

Explanation

This solution builds up each stretched number using bitwise operations. The outer loop iterates i over the numbers to be stretched, from 1 to n, and prints the stretched value after each iteration.

The inner while loop increments s to the number of bits in i, and the subsequent for iterates c over each bit position. Within that loop, d counts up to the number of times to repeat the current bit, which depends on input l. At each step, o is shifted left and the appropriate bit of i is masked off and OR'd in.