

A229219


a(n) = maximal length of partitions of prime(n) into distinct primes.


0



1, 1, 2, 2, 1, 2, 4, 3, 4, 4, 4, 4, 6, 5, 6, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 14, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..74.
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 11
Wikipedia, Knapsack problem


EXAMPLE

a(11) = 4 because prime(11) = 31 = 2 + 3 + 7 + 19, but 31 is not a sum of 5 or more distinct primes.


MATHEMATICA

nn = 20; p = Prime[Range[nn]]; s = Subsets[p]; t2 = Table[Select[s, Total[#] == n &], {n, p}]; Table[Max[Length /@ t2[[n]]], {n, nn}] (* T. D. Noe, Nov 13 2013 *)


CROSSREFS

Cf. A000040, A070215.
Sequence in context: A144963 A305632 A035374 * A048299 A232084 A261359
Adjacent sequences: A229216 A229217 A229218 * A229220 A229221 A229222


KEYWORD

nonn


AUTHOR

Arkadiusz Wesolowski, Nov 10 2013


STATUS

approved



