A266151 Take the binary representation of n, increase each run of 1's by one 1 if the length of run is odd, otherwise, if length of run is even, remove one 1. a(n) is the decimal equivalent of the result.

0, 3, 6, 1, 12, 27, 2, 15, 24, 51, 54, 13, 4, 11, 30, 7, 48, 99, 102, 25, 108, 219, 26, 111, 8, 19, 22, 5, 60, 123, 14, 63, 96, 195, 198, 49, 204, 411, 50, 207, 216, 435, 438, 109, 52, 107, 222, 55, 16, 35, 38, 9, 44, 91, 10, 47, 120, 243, 246, 61, 28, 59, 126, 31

Offset

0,2

Comments

This is a self-inverse permutation of the positive integers.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Index entries for sequences that are permutations of the natural numbers

Example

a(4) = 12 since 4 = 100 binary -> 1100 = 12 decimal,
a(5) = 27 since 5 = 101 binary -> 110011 = 27 decimal,
a(6) = 2 since 6 = 110 binary -> 10 = 2 decimal.

Mathematica

Table[FromDigits[#, 2] &@ Flatten[If[First@ # == 1, If[OddQ@ Length@ #, Append[IntegerDigits@ #, 1], Most@ IntegerDigits@ #], #] & /@ Split@ IntegerDigits[n, 2]], {n, 63}] (* Michael De Vlieger, Dec 22 2015 *)

Prog

(PARI) a(n) = if (n==0, 0, my (b=n%2, r=valuation(n+b, 2), rr=if (b==0, r, r%2, r+1, r-1)); (a(n\2^r)+b)*2^rr-b) \\ Rémy Sigrist, Jan 20 2019

Crossrefs

Cf. A007088, A084483, A162853, A175046, A175047, A175048, A266150.

Sequence in context: A209144 A130724 A120229 * A192100 A123534 A100960

Adjacent sequences: A266148 A266149 A266150 * A266152 A266153 A266154

Keyword

nonn,base

Author

Alex Ratushnyak, Dec 21 2015

Extensions

a(0) = 0 prepended by Rémy Sigrist, Jan 20 2019

Status

approved