A257676 -id:A257676 - cp's OEIS frontend

A257677 Inverse permutation to A257676.

0, 1, 2, 3, 5, 4, 6, 7, 9, 8, 10, 13, 11, 12, 14, 15, 17, 16, 18, 21, 19, 20, 22, 27, 23, 24, 29, 28, 25, 26, 30, 31, 33, 32, 34, 37, 35, 36, 38, 43, 39, 40, 45, 44, 41, 42, 53, 46, 54, 55, 47, 52, 56, 57, 48, 51, 58, 61, 49, 50, 59, 60, 62, 63, 65, 64, 66, 69, 67, 68, 70, 75, 71, 72, 77, 76, 73, 74, 85, 78, 86, 87, 79

Offset: 0

Antti Karttunen, May 04 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8191
Index entries for sequences that are permutations of the natural numbers

Inverse: A257676.

Fixed points: A257678.

A257678 Fixed points of A257676 and A257677.

Original entry on oeis.org

0, 1, 2, 3, 6, 7, 10, 14, 15, 18, 22, 30, 31, 34, 38, 62, 63, 66, 70, 126, 127, 130, 134, 217, 254, 255, 258, 262, 345, 409, 510, 511, 514, 518, 601, 665, 793, 1022, 1023, 1026, 1030, 1113, 1177, 1305, 1561, 2046, 2047, 2050, 2054, 2137, 2201, 2329, 2585, 3097, 3832, 3833, 4094, 4095

Offset: 1

Antti Karttunen, May 04 2015

nonn

Those n for which A257676(n) = n.

Antti Karttunen, Table of n, a(n) for n = 1..678

Subsequence: A000225.

Cf. A257676, A257677.

A218252 Start with 1. For each term m, the next term is the smallest positive integer k such that k - (sum of base 2 digits of k) = m. If no such k exists, use the smallest natural number not already in the sequence.

Original entry on oeis.org

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

Offset: 1

Nico Brown, Oct 24 2012

nonn

The sequence is a permutation of the positive integers.

			To obtain the 2nd term, take the first, 1.  What is the smallest integer k so that k - the number of 1's in k's binary representation is 1? The answer, obviously, is 2. [A213723(1) = 2.]
There is no number that is 2 more than its binary weight [as A213723(2) = 0], therefore we just take 3 as the next term.
Following 3 we can choose either 4 or 5, but 4 is smaller, and is thus the next term of the sequence. [A213723(3) = 4.]

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences that are permutations of the natural numbers

Inverse permutation: A257683.
Cf. A000120, A005187, A011371, A213723, A218253, A218254.
Cf. also A257676.

Name slightly edited and links to A213723 in examples added by Antti Karttunen, May 04 2015

cp's OEIS Frontend

A257677 Inverse permutation to A257676.

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A257678 Fixed points of A257676 and A257677.

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A218252 Start with 1. For each term m, the next term is the smallest positive integer k such that k - (sum of base 2 digits of k) = m. If no such k exists, use the smallest natural number not already in the sequence.

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