A265405 -id:A265405 - cp's OEIS frontend

A265406 a(n) = index of n in A265405 and 0 if n is not present in that sequence.

1, 2, 3, 4, 5, 6, 8, 10, 19, 14, 28, 13, 31, 20, 11, 7, 9, 15, 17, 16, 35, 48, 69, 42, 87, 50, 71, 52, 97, 38, 101, 12, 25, 21, 82, 44, 54, 89, 99, 23, 56, 58, 140, 142, 63, 144, 146, 22, 84, 24, 40, 149, 103, 75, 121, 65

Offset: 1

Antti Karttunen, Dec 29 2015

Cf. A265405.

a(47)-a(56) from Rémy Sigrist, Feb 15 2019

A266351 Start with a(1) = 1, then always choose for a(n) the least unused number such that A057889(a(n)a(n-1)) = A057889(a(n)) A057889(a(n-1)), where A057889 is a bijective base-2 reverse.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 11, 17, 13, 32, 15, 24, 18, 20, 19, 33, 21, 36, 28, 27, 56, 34, 22, 64, 23, 65, 25, 40, 35, 72, 42, 48, 30, 51, 60, 66, 26, 68, 37, 96, 31, 99, 62, 128, 29, 129, 38, 80, 49, 73, 70, 130, 39, 256, 41, 131, 74, 136, 44, 132, 46, 257, 43, 258, 45, 260, 47, 512, 50, 133, 76, 160, 67, 84, 97, 137, 112, 54

Offset: 1

Antti Karttunen, Dec 28 2015

Equally: always choose for a(n) the least unused number such that a(n)*a(n-1) = A057889(A057889(a(n)) * A057889(a(n-1))).
Note that the adjacent terms of permutation A266195 satisfy the same condition, except that permutation is not the lexicographically earliest sequence of this kind (because it has a more restrictive condition). See A266194.
This is a bijection for the same reason that A266195 is. Any high enough 2^k will always save the permutation of being stuck, and will also immediately pick up as its succeeding pair the least term unused so far.

Antti Karttunen, Table of n, a(n) for n = 1..1450
Index entries for sequences that are permutations of the natural numbers

Inverse: A266352.
Cf. A057889, A266194.
Cf. A266195, A265405, A266405 (similar sequences).

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.

Original entry on oeis.org

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

Antti Karttunen, Dec 29 2015

nonn

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.

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

Inverse: A266406.
Cf. A002487.
Cf. A266195, A266351, A265405 (for sequences with similar definitions).

cp's OEIS Frontend

A265406 a(n) = index of n in A265405 and 0 if n is not present in that sequence.

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Extensions

A266351 Start with a(1) = 1, then always choose for a(n) the least unused number such that A057889(a(n)a(n-1)) = A057889(a(n)) A057889(a(n-1)), where A057889 is a bijective base-2 reverse.

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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.

Views

Author

Keywords

Comments

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Crossrefs

cp's OEIS Frontend

A265406 a(n) = index of n in A265405 and 0 if n is not present in that sequence.

Views

Author

Keywords

Crossrefs

Extensions

A266351 Start with a(1) = 1, then always choose for a(n) the least unused number such that A057889(a(n)*a(n-1)) = A057889(a(n)) * A057889(a(n-1)), where A057889 is a bijective base-2 reverse.

Views

Author

Keywords

Comments

Links

Crossrefs

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.

Views

Author

Keywords

Comments

Links

Crossrefs

A266351 Start with a(1) = 1, then always choose for a(n) the least unused number such that A057889(a(n)a(n-1)) = A057889(a(n)) A057889(a(n-1)), where A057889 is a bijective base-2 reverse.

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.