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URL: https://oeis.org/A218469

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A218469
Number of partitions of n into at most three distinct primes (including 1).
2
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.
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
KEYWORD
nonn
AUTHOR
Frank M Jackson, Mar 26 2013
STATUS
approved