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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.
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.
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jul 10 2017
STATUS
approved