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%I #7 Mar 31 2012 13:20:28
%S 5,17,41,461
%N Primes p = Prime[m] such that polynomial (1 + Sum[x^Prime[k],{k,1,m}]) factors over the integers.
%C Corresponding numbers m such that a(n) = Prime[m] are {3,7,13,89,...}. All 4 listed initial terms of a(n) coincide with A007351[n+1].
%C The polynomial is divisible by x^2+1 if and only if p is a member of A007351. - _David Wasserman_, May 20 2008
%C No other terms below 4175. - _Max Alekseyev_, May 31 2008
%e a(1) = 5 because Factor[1+x^2+x^3+x^5] = (x+1)*(x^2+1)*(x^2-x+1), but polynomials (1+x^2) and (1+x^2+x^3) do not factor over the integers.
%e a(2) = 17 because Factor[1+x^2+x^3+x^5+x^7+x^11+x^13+x^17] = (x^2+1)*(x^15-x^13+2x^11-x^9+x^7+x^3+1).
%Y Cf. A038691, A007351.
%K more,nonn
%O 1,1
%A _Alexander Adamchuk_, Sep 13 2006