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

Author

Zhi-Wei Sun, Mar 28 2013

Keywords

• nonn

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.

Examples

			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).
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..350

Crossrefs

Cf. A005117, A217785, A217788, A218465.