A220072 Least prime p such that sum_{k=0}^n A005117(k+1)*x^{n-k} is irreducible modulo p.

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

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