A393980 On the nonnegative integer number line, go to the first next unused power of 2 minus 1, then spiral back to pick up any skipped numbers, and repeat.

0, 1, 3, 2, 7, 4, 6, 5, 15, 8, 14, 9, 13, 10, 12, 11, 31, 16, 30, 17, 29, 18, 28, 19, 27, 20, 26, 21, 25, 22, 24, 23, 63, 32, 62, 33, 61, 34, 60, 35, 59, 36, 58, 37, 57, 38, 56, 39, 55, 40, 54, 41, 53, 42, 52, 43, 51, 44, 50, 45, 49, 46, 48, 47, 127, 64, 126

Offset

0,3

Comments

Permutation of the nonnegative integers.

Links

Ruud H.G. van Tol, Table of n, a(n) for n = 0..10000

Ruud H.G. van Tol, Picture of the first few spirals (svg-file)

Ruud H.G. van Tol, Code for the svg-picture

Index entries for sequences that are permutations of the natural numbers

Formula

a(2^k) = 2^(k+1) - 1.

a(2^k+1) = 2^k.

Example

Sequence as a triangle:
  0;
  1;
  3, 2;
  7, 4, 6, 5;
  15, 8, 14, 9, 13, 10, 12, 11;
  31, 16, 30, 17, 29, 18, 28, 19, 27, 20, 26, 21, 25, 22, 24, 23;
  63, 32, 62, 33, ...

Prog

(PARI) a(n)= if(!n, 0, my(w=logint(n, 2)); if(n%2, n+2^w, 5*2^w-n-2)\2);

Crossrefs

Sequence in context: A316385 A341911 A341916 * A360960 A371974 A344878

Adjacent sequences: A393977 A393978 A393979 * A393981 A393982 A393983

Keyword

nonn,easy,look

Author

Ruud H.G. van Tol, Apr 03 2026

Status

approved