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%I #30 Oct 19 2017 03:13:46
%S 1,2,6,18,30,270,606,123120,888456,23070450,238550160,8282903640,
%T 72789145650,15681266370000,18216437241240
%N a(1) = 1; for n>1, a(n) = smallest integer > a(n-1) such that a(n)*a(i)+1 is prime for all 1 <= i <= n-1.
%C a(16) > 2*10^16.
%C a(n) exists for every n if Dickson's conjecture is true. - _Charles R Greathouse IV_, Nov 30 2012
%H Bill Taylor et al., <a href="https://groups.google.com/forum/?fromgroups=#!topic/sci.math/9bcpPUomW6Y">Sets producing primes</a>, sci.math (2003)
%e After a(1)=1, a(2)=2, a(3)=6, we want m, the smallest number >6 such that m+1, 2m+1 and 6m+1 are all prime: this is m = 18 = a(4).
%t f[s_List] := Block[{k = s[[-1]] + 1, m = s}, While[ Union@ PrimeQ[k*m + 1] != {True}, k++]; Append[s, k]]; Nest[f, {1}, 10] (* _Robert G. Wilson v_, Dec 02 2012 *)
%Y Cf. A219761, A093483.
%K nonn
%O 1,2
%A _Erich Friedman_
%E a(9)-a(13) found by Phil Carmody.
%E a(14)-a(15) from _Don Reble_, Oct 15 2012
%E Edited by _N. J. A. Sloane_, Dec 01 2012
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