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
KEYWORD
nonn
AUTHOR
Frank M Jackson, Mar 26 2013
STATUS
approved