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A117498 Optimal combination of binary and factor methods for finding an addition chain. 1
0, 1, 2, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 6, 6, 7, 6, 7, 5, 6, 6, 7, 6, 7, 7, 7, 6, 7, 7, 8, 7, 7, 8, 9, 6, 7, 7, 7, 7, 8, 7, 8, 7, 8, 8, 9, 7, 8, 8, 8, 6, 7, 7, 8, 7, 8, 8, 9, 7, 8, 8, 8, 8, 9, 8, 9, 7, 8, 8, 9, 8, 8, 9, 9, 8, 9, 8, 9, 9, 9, 10, 9, 7, 8, 8, 8, 8, 9, 8, 9, 8, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
This is an upper bound for both addition chains (A003313) and A117497. The first few values where A003313 is smaller are 23,43,46,47,59. The first few values where A117497 is smaller are 77,143,154,172,173. The first few values where both are smaller are 77,154,172,173,203.
LINKS
FORMULA
a(1)=0; a(n) = min(a(n-1)+1, min_{d|n, 1<d<n} a(d)+a(n/d)). If n is prime, this reduces to a(n) = a(n-1)+1.
EXAMPLE
a(33)=6 because 6 = 1+a(32) < a(3)+a(11) = 2+5. a(36) = min(a(35)+1, a(2)+a(18), a(3)+a(12), a(4)+a(9), a(6)+a(6)) = min(1+7, 1+5, 2+4, 2+4, 3+3) = 6.
CROSSREFS
Sequence in context: A353058 A277608 A117497 * A064097 A014701 A207034
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)