A229219 a(n) = maximal length of partitions of prime(n) into distinct primes.

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

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: A305632 A329069 A035374 * A048299 A232084 A261359

Adjacent sequences: A229216 A229217 A229218 * A229220 A229221 A229222

Keyword

nonn

Author

Arkadiusz Wesolowski, Nov 10 2013

Status

approved