OFFSET
1,2
COMMENTS
The first 7 terms are from Rivera's puzzle 84.
The sequences is infinite [Chris Nash]. - N. J. A. Sloane, Jan 20 2017
LINKS
Chris Nash, Proof that A052349, A128687, and A128688 are infinite [Cached copy of proof, from The Prime Puzzles and Problems website]
Carlos Rivera, Puzzle 84. Non-primes adding up to non-primes, The Prime Puzzles and Problems Connection.
MATHEMATICA
a[1] = 1; a[n_] := a[n] = (s = Subsets[Array[a, n-1], n-1]; c = a[n-1] + 1; While[d = 1; While[!PrimeQ[Total[s[[d]]] + c] && d < Length@s, d++]; d != Length@s || PrimeQ[Total[s[[d]]] + c] || OddQ@c, c++]; c); Array[a, 8] (* Giorgos Kalogeropoulos, Nov 19 2021 *)
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
T. D. Noe, Mar 20 2007
EXTENSIONS
a(11) from Donovan Johnson, Apr 18 2010
a(12) from Donovan Johnson, Jul 06 2010
STATUS
approved