A324400 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 1, where f(n) = -1 if n = 2^k and k > 0, and f(n) = n for all other numbers.

1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 10, 11, 12, 13, 2, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 2, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 2, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78

Offset

1,2

Comments

In the following, A stands for this sequence, A324400, and S -> T (where S and T are sequence A-numbers) indicates that for all i, j >= 1: S(i) = S(i) => T(i) = T(j).

For example, the following chains of implications hold:

A -> A286619 -> A005811,

and

A -> A003602 -> A286622 -> A000120,

-> A286378 -> A002487,

-> A323889,

-> A000593,

-> A001227,

among many others.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

If n <= 3, a(n) = n; and for n >= 4, if A209229(n) = 1, then a(n) = 2, otherwise a(n) = 1 + n - A000523(n).

Prog

(PARI)
A000523(n) = if(n<1, 0, #binary(n)-1);
A324400(n) = if(n<4, n, if(!bitand(n, n-1), 2, 1+n-A000523(n)));

Crossrefs

Cf. A000523.

Cf. A000120, A000265, A000593, A001227, A002487, A003602, A005811, A209229, A286378, A286619, A286622, A294898, A297159, A318311, A323234, A323889, A323904, A324343, A324345 (some of the matching sequences).

Cf. also A103391, A295300, A305800, A305801, A324401.

Sequence in context: A324346 A323904 A325810 * A297157 A304492 A305303

Adjacent sequences: A324397 A324398 A324399 * A324401 A324402 A324403

Keyword

nonn

Author

Antti Karttunen, Mar 01 2019

Status

approved