A294734 Lexicographically earliest sequence of distinct positive odd numbers such that, for any n > 1, n divides a(n-1) + a(n).

1, 3, 9, 7, 13, 5, 23, 17, 19, 11, 33, 15, 37, 47, 43, 21, 81, 27, 49, 31, 53, 35, 57, 39, 61, 69, 93, 75, 41, 79, 45, 51, 147, 91, 119, 25, 123, 29, 127, 73, 173, 121, 137, 83, 97, 87, 101, 139, 155, 95, 109, 99, 113, 103, 117, 107, 235, 55, 63, 177, 67, 181

Offset

1,2

Comments

This sequence is a variant of A099506 and of A134204.

The variant where "n divides a(n) + a(n+1)" corresponds to A005408 (the odd numbers).

Empirically, the scatterplot of the first terms shows a bundle of curves that correspond to terms sharing the same value of Sum_{k=2.. n} ((-1)^k (a(k+1) + a(k))/k) (see Links section); the sequence A134204 has similar features.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored scatterplot of the first 10000 terms

Rémy Sigrist, Colored scatterplot of the first 100000 terms

Rémy Sigrist, PARI program for A294734

Prog

(PARI) See Links section.

Crossrefs

Cf. A005408, A099506, A134204.

Sequence in context: A362150 A267363 A146179 * A214661 A178414 A220654

Adjacent sequences: A294731 A294732 A294733 * A294735 A294736 A294737

Keyword

nonn

Author

Rémy Sigrist, Nov 07 2017

Status

approved