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%I #8 Feb 12 2015 11:36:24
%S 3,5,7,83,317,383,2111,2423,3797,8117,12143,18959,24077,33311,89561,
%T 142979,161309,191339,218531,234629,278981,297263,516911,731957,
%U 746777,882029,908627,953789,1245551,1279361,1790339,2550059,2638667
%N The slowest increasing sequence of primes such that no three terms sum up to a prime number.
%C Start with s={3,5,7}. Then a(n) is the least prime > a(n-1) such that no three terms sum up to a prime number.
%H Zak Seidov, <a href="/A254925/b254925.txt">Table of n, a(n) for n = 1..104</a>
%t s = {3, 5, 7}; bs = {8, 10, 12}; p = 7; Do[Label[np]; p = NextPrime[p];
%t Do[If[PrimeQ[p + bs[[k]]], Goto[np]], {k, Length[bs]}]; AppendTo[s, p]; bs = Join[bs, s + p]; Print[p], {100}]
%K nonn
%O 1,1
%A _Zak Seidov_, Feb 10 2015