A218469 Number of partitions of n into at most three distinct primes (including 1).

1, 1, 2, 1, 2, 2, 2, 3, 2, 3, 2, 3, 3, 4, 3, 4, 3, 5, 5, 6, 5, 5, 5, 6, 6, 6, 5, 4, 6, 6, 9, 7, 7, 6, 8, 7, 10, 6, 8, 5, 10, 8, 12, 9, 10, 7, 13, 9, 14, 10, 12, 7, 15, 9, 17, 9, 13, 6, 17, 10, 21, 10, 15, 8, 19, 11, 22, 9, 16, 8, 24, 12, 25, 12, 19, 10, 26, 12

Offset

1,3

Comments

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

Links

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

Example

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

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]]&&Total[Intersection[parts[[n]]]]==Total[parts
  [[1]]], count++]; n++]; count); Table[goldbachcount[i], {i, 1, 100}]

Crossrefs

Cf. A002375, A025583, A068307, A071335, A185101, A218007.

Sequence in context: A274701 A184956 A340134 * A343333 A230502 A280253

Adjacent sequences: A218466 A218467 A218468 * A218470 A218471 A218472

Keyword

nonn

Author

Frank M Jackson, Mar 26 2013

Status

approved