A225607 If the run lengths of the binary representation of n are [1+r_1, 1+r_2, 1+r_3, ..., 1+r_k], then those of a(n) are [1+(r_1), 1+(r_1 XOR r_2), 1+(r_2 XOR r_3), ..., 1+(r_{k-1} XOR r_k)], where XOR denotes the XOR binary operator.

1, 2, 3, 4, 5, 12, 7, 8, 19, 10, 11, 6, 25, 56, 15, 16, 71, 38, 9, 20, 21, 44, 23, 48, 27, 50, 51, 112, 113, 240, 31, 32, 271, 142, 143, 76, 77, 36, 79, 40, 83, 42, 43, 22, 89, 184, 47, 24, 391, 54, 13, 100, 101, 204, 103, 14, 451, 226, 227, 120, 481, 992, 63

Offset: 1

Author

Paul Tek, Aug 06 2013

Keywords

• nonn
• base

Comments

Inverse permutation of A227987.

Examples

			For n=28927:
(1) binary representation of n = "111000011111111",
(2) run lengths of n = [1+2,1+3,1+7],
(3) run lengths of a(n) = [1+2,1+(2 XOR 3),1+(3 XOR 7)]=[3,2,5],
(4) binary representation of a(n) = "1110011111",
(5) a(n) = 927.
		

Links

• Paul Tek, Table of n, a(n) for n = 1..10000
• Paul Tek, PERL program for this sequence
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A227987, A226569.

Programs

Perl

See Link section.