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

%I #12 Nov 11 2017 11:53:15

%S 1,3,9,7,13,5,23,17,19,11,33,15,37,47,43,21,81,27,49,31,53,35,57,39,

%T 61,69,93,75,41,79,45,51,147,91,119,25,123,29,127,73,173,121,137,83,

%U 97,87,101,139,155,95,109,99,113,103,117,107,235,55,63,177,67,181

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

%C This sequence is a variant of A099506 and of A134204.

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

%C 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.

%H Rémy Sigrist, <a href="/A294734/b294734.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A294734/a294734.png">Colored scatterplot of the first 10000 terms</a>

%H Rémy Sigrist, <a href="/A294734/a294734_1.png">Colored scatterplot of the first 100000 terms</a>

%H Rémy Sigrist, <a href="/A294734/a294734.gp.txt">PARI program for A294734</a>

%o (PARI) See Links section.

%Y Cf. A005408, A099506, A134204.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Nov 07 2017