A266150 Take the binary representation of n, increase each run of 0's by one 0 if the length of run is odd, otherwise, if length of run is even, remove one 0. a(n) is the decimal equivalent of the result.

0, 1, 4, 3, 2, 9, 12, 7, 16, 5, 36, 19, 6, 25, 28, 15, 8, 33, 20, 11, 18, 73, 76, 39, 48, 13, 100, 51, 14, 57, 60, 31, 64, 17, 132, 67, 10, 41, 44, 23, 144, 37, 292, 147, 38, 153, 156, 79, 24, 97, 52, 27, 50, 201, 204, 103, 112, 29, 228, 115, 30, 121, 124, 63, 32

Offset: 0

Author

Alex Ratushnyak, Dec 21 2015

Keywords

• nonn
• base

Comments

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

Examples

			a(4) = 2 since 4 = 100 binary -> 10 = 2 decimal.
a(5) = 9 since 5 = 101 binary -> 1001 = 9 decimal.
a(6) = 12 since 6 = 110 binary -> 1100 = 12 decimal.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A007088, A084483, A162853, A175046, A175047, A175048, A266151.

Programs

Mathematica

Table[FromDigits[#, 2] &@ Flatten[If[First@ # == 0, If[OddQ@ Length@ #, Append[IntegerDigits@ #, 0], Most@ IntegerDigits@ #], #] & /@ Split@ IntegerDigits[n, 2]], {n, 64}] (* Michael De Vlieger, Dec 22 2015 *)

PARI

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

Extensions

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