A289726 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, multiplying n by a(n) does not produce any carries when performed in base 2.

1, 2, 4, 3, 6, 5, 8, 7, 10, 9, 16, 17, 32, 18, 33, 11, 12, 14, 20, 19, 24, 34, 64, 21, 40, 65, 66, 36, 128, 68, 129, 13, 15, 22, 72, 28, 48, 80, 130, 25, 96, 67, 256, 132, 136, 257, 258, 37, 73, 133, 160, 260, 512, 264, 513, 137, 514, 516, 520, 272, 1024, 528

Offset

1,2

Comments

This sequence is a self-inverse permutation of the natural numbers.

A priori, there are only two fixed points: 1 and 2 (note that a fixed point must be a power of 2).

This sequence is related to A266195: here n * a(n), there a(n) * a(n+1), does not produce any carries when performed in base 2.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A289726

Index entries for sequences that are permutations of the natural numbers

Example

1 * 1 can be computed without carry in base 2, hence a(1) = 1.
2 * 2 can be computed without carry in base 2, hence a(2) = 2.
3 * 3 cannot be computed without carry in base 2.
3 * 4 can be computed without carry in base 2, hence a(3) = 4.

Prog

(PARI) See Links section.

Crossrefs

Cf. A266195.

Sequence in context: A114112 A113981 A234519 * A308598 A343012 A143692

Adjacent sequences: A289723 A289724 A289725 * A289727 A289728 A289729

Keyword

nonn,base

Author

Rémy Sigrist, Jul 10 2017

Status

approved