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 A220072 Least prime p such that sum_{k=0}^n A005117(k+1)*x^{n-k} is irreducible modulo p. 11
 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, 239, 31, 337, 487, 97, 337, 97, 307, 181, 223, 19, 79, 401, 2, 491, 269, 211, 97, 193, 719, 149, 97, 191, 83, 613 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. For another related conjecture, see the author's comment on A005117. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..350 EXAMPLE 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). CROSSREFS Cf. A005117, A217785, A217788, A218465. Sequence in context: A246355 A016580 A309324 * A065223 A248154 A274415 Adjacent sequences:  A220069 A220070 A220071 * A220073 A220074 A220075 KEYWORD nonn AUTHOR Zhi-Wei Sun, Mar 28 2013 STATUS approved

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Last modified December 14 05:36 EST 2019. Contains 329978 sequences. (Running on oeis4.)