A266405 -id:A266405 - cp's OEIS frontend

A266406 Inverse permutation to A266405.

1, 2, 3, 4, 5, 8, 6, 7, 9, 10, 13, 16, 15, 11, 18, 12, 14, 17, 22, 24, 41, 27, 21, 20, 32, 19, 28, 25, 30, 36, 31, 23, 29, 26, 39, 35, 45, 47, 56, 60, 51, 43, 110, 55, 33, 48, 63, 38, 34, 81, 67, 37, 96, 50, 61, 59, 75, 83, 65, 71, 77, 82, 76, 40, 62, 49, 112, 58, 42, 69, 73, 70, 104, 135, 182, 153, 114, 290, 125, 74, 173, 53, 52

Offset: 1

Antti Karttunen, Dec 29 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..148 [If you compute more terms for the b-file, then please upgrade the b-file of A266405 as well, thanks!]
Index entries for sequences that are permutations of the natural numbers

Cf. A266405.

Scheme
```
;; Use the code given in A266405.
```

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).

A265405 Start with a(1) = 1, then always choose for a(n) the least unused number such that A193231(a(n)a(n-1)) = A193231(a(n)) A193231(a(n-1)), where A193231 is an involution of natural numbers called Blue code.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 16, 7, 17, 8, 15, 32, 12, 10, 18, 20, 19, 256, 9, 14, 34, 48, 40, 50, 33, 60, 257, 11, 97, 258, 13, 101, 209, 65536, 21, 259, 64, 30, 65, 51, 80, 24, 84, 36, 85, 66, 260, 22, 4352, 26, 4368, 28, 4369, 37, 768, 41, 770, 42, 771, 68, 90, 272, 45, 273, 56, 1200, 952, 4096, 23, 4097, 27, 4098, 86, 512, 54

Offset: 1

Antti Karttunen, Dec 29 2015

Does this sequence die after a(144) = 46 ?
No, a(145) = 16777216, but whether the sequence is finished remains open. - Rémy Sigrist, Feb 15 2019
The next unused number of the form 2^2^k is always a valid choice, so this sequence is infinite. - Charlie Neder, Apr 14 2019

Rémy Sigrist, Table of n, a(n) for n = 1..183 (first 144 terms from Antti Karttunen) [More terms needed for b-file.]
Rémy Sigrist, PARI program for A265405

Inverse: A265406.
Cf. A193231.
Cf. A266195, A266351, A266405 (sequences with similar definitions, of which at least the first two are known to be infinite and also bijective).

PARI
```
See Links section.
```

A266413 a(1) = 1, after which each a(n) = A002487(n)-th number selected from those not yet in the sequence.

Original entry on oeis.org

1, 2, 4, 3, 7, 6, 9, 5, 12, 11, 15, 10, 17, 14, 18, 8, 21, 20, 25, 19, 28, 24, 29, 16, 31, 27, 34, 23, 35, 30, 33, 13, 38, 37, 43, 36, 47, 42, 48, 32, 51, 46, 55, 41, 56, 49, 53, 26, 57, 52, 62, 45, 65, 59, 64, 40, 66, 60, 69, 50, 68, 58, 63, 22, 71, 70, 77, 67, 82, 76, 83, 61, 87, 81, 92, 75, 93, 84, 89, 54, 94, 88, 101, 80

Offset: 1

Antti Karttunen, Dec 29 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16385
Index entries for sequences that are permutations of the natural numbers

Inverse: A266414.
Cf. A002487.
Similar permutations in Quetian style: A119435, A126917, A246165, A266411.
Cf. also A266405.

f[n_] := Block[{a = {1}, g, b = Range[2, n]}, g[1] = 1; g[x_] := g[x] = If[EvenQ@ x, g[x/2], g[(x - 1)/2] + g[(x + 1)/2]]; Do[{AppendTo[a, #[[1, 1]]], Set[b, Last@ #]} &@ If[# > Length@ b, Break[], TakeDrop[b, {#}]] &@ g@ k, {k, 2, n}]; a]; f@ 103 (* Michael De Vlieger, Dec 29 2015, Version 10.2, after N. J. A. Sloane at A002487 *)

cp's OEIS Frontend

A266406 Inverse permutation to A266405.

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Scheme

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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Crossrefs

A265405 Start with a(1) = 1, then always choose for a(n) the least unused number such that A193231(a(n)a(n-1)) = A193231(a(n)) A193231(a(n-1)), where A193231 is an involution of natural numbers called Blue code.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A266413 a(1) = 1, after which each a(n) = A002487(n)-th number selected from those not yet in the sequence.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

cp's OEIS Frontend

A266406 Inverse permutation to A266405.

Views

Author

Keywords

Links

Crossrefs

Programs

Scheme

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

A265405 Start with a(1) = 1, then always choose for a(n) the least unused number such that A193231(a(n)*a(n-1)) = A193231(a(n)) * A193231(a(n-1)), where A193231 is an involution of natural numbers called Blue code.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A266413 a(1) = 1, after which each a(n) = A002487(n)-th number selected from those not yet in the sequence.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

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.

A265405 Start with a(1) = 1, then always choose for a(n) the least unused number such that A193231(a(n)a(n-1)) = A193231(a(n)) A193231(a(n-1)), where A193231 is an involution of natural numbers called Blue code.