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A328444
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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.
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4
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) <= Sum_{k = 1..n-1} a(k) for any n > 2.
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EXAMPLE
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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.
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PROG
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(PARI) See Links section.
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CROSSREFS
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See A328443 for a similar sequence.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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