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

Author

Rémy Sigrist, Nov 07 2017

Keywords

• nonn

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

Crossrefs

Cf. A005408, A099506, A134204.

Programs

PARI

See Links section.