A341911 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the number of ones in the binary expansion of n equals the number of runs in the binary expansion of a(n).

0, 1, 3, 2, 7, 4, 6, 5, 15, 8, 12, 9, 14, 11, 13, 10, 31, 16, 24, 17, 28, 19, 23, 18, 30, 25, 27, 20, 29, 22, 26, 21, 63, 32, 48, 33, 56, 35, 39, 34, 60, 47, 49, 36, 51, 38, 40, 37, 62, 55, 57, 44, 59, 46, 50, 41, 61, 52, 54, 43, 58, 45, 53, 42, 127, 64, 96

Offset

0,3

Comments

This sequence is a permutation of the nonnegative integers with inverse A341910.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

Rémy Sigrist, Colored scatterplot of the first 2^16 terms (where the color is function of A000120(n))

Rémy Sigrist, PARI program for A341911

Index entries for sequences related to binary expansion of n

Index entries for sequences that are permutations of the natural numbers

Formula

A000120(n) = A005811(a(n)).

a(n) < 2^k for any n < 2^k.

Example

The first terms, in decimal and in binary, are:
  n   a(n)  bin(n)   bin(a(n))
  --  ----  -------  ---------
   0     0        0          0
   1     1        1          1
   2     3       10         11
   3     2       11         10
   4     7      100        111
   5     4      101        100
   6     6      110        110
   7     5      111        101
   8    15     1000       1111
   9     8     1001       1000
  10    12     1010       1100

Mathematica

Block[{a = {0}, k}, Do[k = 1; While[Nand[FreeQ[a, k], Length[Split@ IntegerDigits[k, 2]] == #], k++] &@ DigitCount[i, 2, 1]; AppendTo[a, k], {i, 66}]; a] (* Michael De Vlieger, Feb 24 2021 *)

Prog

(PARI) See Links section.

Crossrefs

Cf. A000120, A005811, A298847, A341910 (inverse).

Sequence in context: A191664 A118319 A316385 * A341916 A360960 A371974

Adjacent sequences: A341908 A341909 A341910 * A341912 A341913 A341914

Keyword

nonn,look,base

Author

Rémy Sigrist, Feb 23 2021

Status

approved