A227987 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_1 XOR r_2 XOR r_3), ..., 1+(r_1 XOR ... XOR r_k)], where XOR denotes the XOR binary operator.

1, 2, 3, 4, 5, 12, 7, 8, 19, 10, 11, 6, 51, 56, 15, 16, 71, 76, 9, 20, 21, 44, 23, 48, 13, 204, 25, 112, 455, 240, 31, 32, 271, 568, 143, 38, 307, 18, 79, 40, 83, 42, 43, 22, 179, 184, 47, 24, 783, 26, 27, 102, 819, 50, 207, 14, 1807, 3640, 911, 120, 3855

Offset

1,2

Comments

This is a permutation of the natural numbers with inverse permutation A225607.

The sequence (n, a(n), a(a(n)), a(a(a(n))),...) is periodic for any n.

The run lengths of the binary representation of a fixed point are of the form [1, 1,...,1, K] (any number of ones followed by any number).

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

Example

For n=927:
(1) binary representation of n = "1110011111",
(2) run lengths of n = [1+2,1+1,1+4],
(3) run lengths of a(n) = [1+(2),1+(2 XOR 1),1+(2 XOR 1 XOR 4)]=[3,4,8],
(4) binary representation of a(n) = "111000011111111",
(5) a(n) = 28927.

Prog

(Perl) See Links section.

Crossrefs

Cf. A056539, A226532, A225607 (inverse).

Sequence in context: A064446 A352257 A225607 * A261863 A327262 A344370

Adjacent sequences: A227984 A227985 A227986 * A227988 A227989 A227990

Keyword

nonn,base

Author

Paul Tek, Aug 02 2013

Status

approved