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

Author

Rémy Sigrist, Jul 10 2017

Keywords

• nonn
• base

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.

Examples

			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.
		

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

Crossrefs

Cf. A266195.

Programs

PARI

See Links section.