A338630 Least number of odd primes that add up to n, or 0 if no such representation is possible.

0, 0, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 2, 3, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2

Offset

1,6

Links

Table of n, a(n) for n=1..110.

Eric Weisstein's World of Mathematics, Prime Partition

Index entries for sequences related to Goldbach conjecture

Example

a(9) = 3 because 9 = 3 + 3 + 3 is a partition of 9 into 3 odd prime parts and there is no such partition with fewer terms.

Mathematica

Block[{f, a}, f[m_] := Block[{s = {Prime@ PrimePi@ m}}, KeySort@ Merge[#, Identity] &@ Reap[Do[If[# <= m, Sow[# -> s]; AppendTo[s, Last@ s], If[Last@ s == 3, s = DeleteCases[s, 3]; If[Length@ s == 0, Break[], s = MapAt[Prime[PrimePi[#] - 1] &, s, -1]], s = MapAt[Prime[PrimePi[#] - 1] &, s, -1]]] &@ Total[s], {i, Infinity}]][[-1, -1]] ]; a = f[105]; Array[If[KeyExistsQ[a, #], Min@ Map[Length, Lookup[a, #]], 0] &, Max@ Keys@ a]] (* Michael De Vlieger, Nov 04 2020 *)

Crossrefs

Cf. A051034, A065091.

Sequence in context: A329744 A277889 A018194 * A286281 A229830 A105203

Adjacent sequences: A338627 A338628 A338629 * A338631 A338632 A338633

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 04 2020

Status

approved