A328444 Lexicographically earliest sequence of distinct positive numbers such that a(1) = 1, a(2) = 2, and for n > 2, a(n) divides Sum_{i = n-k..n-1} a(i) with k > 0 as small as possible.

1, 2, 3, 5, 4, 9, 13, 11, 6, 17, 23, 8, 31, 39, 7, 46, 53, 33, 43, 19, 62, 27, 89, 29, 59, 22, 81, 103, 92, 15, 107, 61, 12, 73, 85, 79, 41, 10, 51, 34, 95, 129, 14, 143, 157, 20, 177, 197, 187, 16, 203, 219, 211, 86, 99, 37, 68, 21, 18, 24, 42, 66, 36, 102

Offset

1,2

Comments

When computing a(n) for n > 2, there may be candidates for different values of k; we choose the candidate that minimizes k.

This sequence is an infinite variant of A085947; a(n) = A085947(n) for n = 1..39.

Links

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

Rémy Sigrist, PARI program for A328444

Formula

a(n) <= Sum_{k = 1..n-1} a(k) for any n > 2.

Example

For n = 3:
- the divisors of a(2) = 2 are all already in the sequence,
- 3 is the least divisor of a(1) + a(2) = 1 + 2 = 3 not yet in the sequence,
- so a(3) = 3.
For n = 4:
- the divisors of a(3) = 3 are all already in the sequence,
- 5 is the least divisor of a(2) + a(3) = 2 + 3 = 5 not yet in the sequence,
- so a(3) = 5.
For n = 5:
- the divisors of a(4) = 5 are all already in the sequence,
- 4 is the least divisor of a(3) + a(4) = 3 + 5 = 8 not yet in the sequence,
- so a(5) = 4.

Prog

(PARI) \\ See Links section.

Crossrefs

See A328443 for a similar sequence.

Cf. A085947.

Sequence in context: A365642 A353082 A085947 * A332301 A360281 A069202

Adjacent sequences: A328441 A328442 A328443 * A328445 A328446 A328447

Keyword

nonn

Author

Rémy Sigrist, Oct 15 2019

Status

approved