A266405 Start with a(1) = 1, then always choose for a(n) the least unused number such that A002487(a(n)*a(n-1)) = A002487(a(n)) * A002487(a(n-1)), where A002487 is Stern-Brocot sequence.

1, 2, 3, 4, 5, 7, 8, 6, 9, 10, 14, 16, 11, 17, 13, 12, 18, 15, 26, 24, 23, 19, 32, 20, 28, 34, 22, 27, 33, 29, 31, 25, 45, 49, 36, 30, 52, 48, 35, 64, 21, 69, 42, 128, 37, 256, 38, 46, 66, 54, 41, 83, 82, 108, 44, 39, 88, 68, 56, 40, 55, 65, 47, 130, 59, 96, 51, 192, 70, 72, 60, 104, 71, 80, 57, 63, 61, 126, 98, 90, 50, 62, 58, 124, 100, 121, 127

Offset: 1

Author

Antti Karttunen, Dec 29 2015

Keywords

• nonn

Comments

This is a permutation of natural numbers for the same reason that A266195 and A266351 are. If nothing else works for the value of next a(n), then at least the next unused power of 2 will save the sequence from dying, and will also immediately pick up as its succeeding pair the least term not used so far. This follows because A002487(2^m) = 1 and A002487(2^m * n) = A002487(n) for all n and m.

Still, it would be nice to know when 149 will appear in the sequence.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2016
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A266406.

Cf. A002487.

Cf. A266195, A266351, A265405 (for sequences with similar definitions).