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A128688
a(1)=1. For n>1, a(n) is the smallest even number such that every subset of a(1), ..., a(n) adds to a nonprime.
3
1, 8, 24, 86, 90, 780, 5940, 52350, 278460, 40768260, 6847205430, 5027286840810
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
Cf. A052349 (no restrictions on even or odd), A128687 (restricted to odd numbers).
Sequence in context: A296400 A297808 A097544 * A279162 A217016 A019260
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