A218007 Number of partitions of n into at most three primes (including 1).

1, 2, 3, 3, 4, 4, 5, 4, 5, 4, 5, 4, 6, 5, 7, 5, 7, 5, 8, 6, 9, 6, 9, 7, 10, 7, 10, 5, 10, 6, 12, 7, 13, 7, 12, 8, 14, 7, 14, 6, 15, 8, 17, 9, 17, 8, 18, 10, 19, 10, 19, 7, 20, 9, 21, 9, 20, 7, 21, 11, 25, 11, 24, 9, 26, 11, 27, 9, 24, 8, 28, 12, 30, 13, 29

Offset

1,2

Comments

The above sequence relies on the strong Goldbach's conjecture that any positive integer is the sum of at most three distinct terms from {1 union primes}.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Example

a(21)=9 as 21 = 1+1+19 = 2+19 = 1+3+17 = 2+2+17 = 1+7+13 = 3+5+13 = 3+7+11 = 5+5+11 = 7+7+7

Mathematica

primeQ[p0_] := If[p0==1, True, PrimeQ[p0]]; SetAttributes[primeQ, Listable]; goldbachcount[p1_] := (parts=IntegerPartitions[p1, 3]; count=0; n=1; While[n<=Length[parts], If[Intersection[Flatten[primeQ[parts[[n]]]]][[1]] == True, count++]; n++]; count); Table[goldbachcount[i], {i, 1, 100}]
Table[Length[Select[#/.(1->2)&/@IntegerPartitions[n, 3], AllTrue[#, PrimeQ]&]], {n, 80}] (* Harvey P. Dale, Jan 11 2023 *)

Crossrefs

Cf. A002375, A025583, A068307, A071335, A185101.

Sequence in context: A064066 A297025 A325134 * A060607 A265690 A061339

Adjacent sequences: A218004 A218005 A218006 * A218008 A218009 A218010

Keyword

nonn

Author

Frank M Jackson, Mar 26 2013

Status

approved