A257798 Permutation of natural numbers: a(1) = 1; a(2n) = nontriangular(a(n)), a(2n+1) = triangular(1+a(n)), where triangular = A000217, nontriangular = A014132.

1, 2, 3, 4, 6, 5, 10, 7, 15, 9, 28, 8, 21, 14, 66, 11, 36, 20, 136, 13, 55, 35, 435, 12, 45, 27, 253, 19, 120, 77, 2278, 16, 78, 44, 703, 26, 231, 152, 9453, 18, 105, 65, 1596, 43, 666, 464, 95266, 17, 91, 54, 1081, 34, 406, 275, 32385, 25, 210, 135, 7381, 89, 3081, 2345, 2598060, 22, 153, 90, 3160, 53, 1035, 740, 248160, 33

Offset: 1

Author

Antti Karttunen, May 18 2015

Keywords

• nonn

Comments

This sequence can be represented as a binary tree. Each left hand child is produced as A014132(n) and each right hand child as A000217(1+n), when a parent contains n >= 1:

1

................../ \..................

2 3

4......../ \........6 5......../ \.......10

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

7 15 9 28 8 21 14 66

11 36 20 136 13 55 35 435 12 45 27 253 19 120 77 2278

etc.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1024
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A257797.

Cf. A000217, A014132.

Cf. also permutation A183079.

Formula

a(1)=1; after which: a(2n) = A014132(a(n)), a(2n+1) = A000217(a(n)+1).