A122035 Primes p = Prime[m] such that polynomial (1 + Sum[x^Prime[k],{k,1,m}]) factors over the integers.

5, 17, 41, 461

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^2-x+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^15-x^13+2x^11-x^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