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

Author

Rémy Sigrist, Oct 15 2019

Keywords

• nonn

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.

Examples

			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.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A328444

Crossrefs

See A328443 for a similar sequence.

Cf. A085947.

Programs

PARI

\\ See Links section.

Formula

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