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A350029 Write n as n = k1 + k2 + ... + km, so that all k are distinct positive integers. a(n) is the maximum value of A001055(k1) + A001055(k2) + ... + A001055(km) over all such partitions. 2
1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
There exist cases where a(n) < a(n-1). Some examples are n = 53, 77, 113, 125, ...
There may exist multiple partitions of n = k1 + k2 + ... + km, where a(n) = A001055(k1) + A001055(k2) + ... + A001055(km). The number of such partitions is A350032(n).
It appears that a(n) - log(A066739(n)) > 0.
If the definition of this sequence would allow k1 = k2 = km, then this sequence would be the trivial sequence a(n) = n instead.
LINKS
Thomas Scheuerle, Examples for n = 1 to 100.
EXAMPLE
n = k1+k2+...+km A001055(k1)+...+A001055(km) = a(n)
--------------------------------------------------------
1 = 1 1 = 1
2 = 2 1 = 1
3 = 1 + 2 1 + 1 = 2
4 = 1 + 3 1 + 1 = 2
5 = 1 + 4 1 + 2 = 3
6 = 1 + 2 + 3 1 + 1 + 1 = 3
PROG
(PARI) A350029(n, K=0) = { my(a=A001055(n)); while(n>2*K+=1, a=max(A001055(K)+A350029(n-K, K), a) ); a } \\ M. F. Hasler, Dec 09 2021
CROSSREFS
Sequence in context: A084557 A024417 A060021 * A000006 A061017 A331535
KEYWORD
nonn
AUTHOR
Thomas Scheuerle, Dec 09 2021
STATUS
approved

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)