

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



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



KEYWORD

nonn


AUTHOR



STATUS

approved



