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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
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
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
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Mar 28 2013
STATUS
approved