

A122035


Primes p = Prime[m] such that polynomial (1 + Sum[x^Prime[k],{k,1,m}]) factors over the integers.


1




OFFSET

1,1


COMMENTS

Corresponding numbers m such that a(n) = Prime[m] are {3,7,13,89,...}. All 4 listed initial terms of a(n) coincide with A007351[n+1].
The polynomial is divisible by x^2+1 if and only if p is a member of A007351.  David Wasserman, May 20 2008
No other terms below 4175.  Max Alekseyev, May 31 2008


LINKS

Table of n, a(n) for n=1..4.


EXAMPLE

a(1) = 5 because Factor[1+x^2+x^3+x^5] = (x+1)*(x^2+1)*(x^2x+1), but polynomials (1+x^2) and (1+x^2+x^3) do not factor over the integers.
a(2) = 17 because Factor[1+x^2+x^3+x^5+x^7+x^11+x^13+x^17] = (x^2+1)*(x^15x^13+2x^11x^9+x^7+x^3+1).


CROSSREFS

Cf. A038691, A007351.
Sequence in context: A346706 A106973 A102264 * A052350 A318826 A239195
Adjacent sequences: A122032 A122033 A122034 * A122036 A122037 A122038


KEYWORD

more,nonn


AUTHOR

Alexander Adamchuk, Sep 13 2006


STATUS

approved



