

A220072


Least prime p such that sum_{k=0}^n A005117(k+1)*x^{nk} 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
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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^{nk} over the rationals is isomorphic to the symmetric group S_n.
For another related conjecture, see the author's comment on A005117.


LINKS

ZhiWei 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)==(x2)*(x^3x^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

ZhiWei Sun, Mar 28 2013


STATUS

approved



