A319579 Lexicographically earliest infinite sequence of positive terms such that for any n >= 0, a(n+1) = a(n + a(n)) - a(n).

2, 2, 4, 6, 2, 8, 10, 2, 6, 8, 2, 5, 7, 18, 14, 8, 12, 10, 2, 25, 27, 2, 18, 20, 2, 4, 6, 12, 22, 10, 24, 32, 18, 14, 15, 2, 5, 7, 45, 34, 38, 12, 3, 22, 52, 25, 2, 29, 31, 17, 32, 3, 53, 15, 56, 2, 2, 4, 6, 4, 46, 10, 10, 50, 10, 74, 49, 8, 71, 52, 27, 20, 60

Offset

0,1

Comments

The smallest legal term is 2, otherwise for a(n) = 1: a(n+1) = a(n + 1) - 1.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, C++ program for A319579

Rémy Sigrist, Scatterplot of the first 100000 terms

Formula

a(n+1) = a(n + a(n)) - a(n).

Example

a(0) = 2, because it's the smallest positive integer that satisfies the rule a(n+1) = a(n + a(n)) - a(n).
a(1) = 2, because we have again free choice inside the rules.
a(2) = 4, because a(1) = a(0 + a(0)) - a(0) = a(0 + 2) - a(0) = a(2) - 2 = 2.
a(3) = 6, because a(2) = a(1 + a(1)) - a(1) = a(1 + 2) - a(1) = a(3) - 2 = 4.
a(6) = 10, because a(3) = a(2 + a(2)) - a(2) = a(2 + 4) - a(2) = a(6) - 4 = 6.
a(4) = 2, because we have again free choice inside the rules.
And so on.

Prog

(C++) See Links section.

Crossrefs

Cf. A309681.

Sequence in context: A238959 A238972 A207193 * A286631 A286243 A368259

Adjacent sequences: A319576 A319577 A319578 * A319580 A319581 A319582

Keyword

nonn

Author

Marc Morgenegg, Aug 27 2019

Extensions

Name amended by Rémy Sigrist, Oct 01 2019

Status

approved