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%I #37 Mar 28 2013 11:45:19
%S 2,5,2,7,11,31,13,19,89,17,37,37,43,19,137,29,3,7,2,19,13,59,139,37,2,
%T 239,31,337,487,97,337,97,307,181,223,19,79,401,2,491,269,211,97,193,
%U 719,149,97,191,83,613
%N Least prime p such that sum_{k=0}^n A005117(k+1)*x^{n-k} is irreducible modulo p.
%C Conjecture: For any n>0, we have a(n) <= n*(n+1), and the Galois group of SF_n(x) = sum_{k=0}^n A005117(k+1)*x^{n-k} over the rationals is isomorphic to the symmetric group S_n.
%C For another related conjecture, see the author's comment on A005117.
%H Zhi-Wei Sun, <a href="/A220072/b220072.txt">Table of n, a(n) for n = 1..350</a>
%e a(4)=7 since SF_4(x)=x^4+2x^3+3x^2+5x+6 is irreducible modulo 7 but reducible modulo any of 2, 3, 5. It is easy to check that SF_4(x)==(x-2)*(x^3-x^2+x+2) (mod 5).
%Y Cf. A005117, A217785, A217788, A218465.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Mar 28 2013
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