A099408 a(n) is the smallest prime p such that x^2+n has roots in the p-adic integers.

5, 3, 7, 5, 3, 5, 2, 3, 5, 7, 3, 7, 7, 3, 2, 5, 3, 3, 5, 3, 5, 13, 2, 5, 5, 3, 7, 2, 3, 11, 2, 3, 7, 5, 3, 5, 19, 3, 2, 7, 3, 13, 11, 3, 3, 5, 2, 7, 5, 3, 5, 7, 3, 5, 2, 3, 11, 31, 3, 2, 5, 3, 2, 5, 3, 5, 17, 3, 5, 17, 2, 3, 7, 3, 7, 5, 3, 19, 2, 3, 5, 7, 3, 5, 11, 3, 2, 13, 3, 7, 5, 2, 17, 5, 2, 5, 7, 3

Offset

1,1

Links

Table of n, a(n) for n=1..98.

Example

a(7)=2 because x^2+7 has roots in the 2-adic integers. Roots are 1 + 2^2 + 2^4 + 2^5 + 2^7 + O(2^9) and 1 + 2 + 2^3 + 2^6 + 2^8 + O(2^9).

Maple

p:=1; anz:=0; while anz=0 do p:=nextprime(p); poly:=x^2+i; anz:=nops([rootp(poly, p)]); od; a(n):=p;

Prog

(PARI) { a(n) = forprime(p=2, 10^5, if(!polisirreducible((x^2+n)*(1+O(p))), return(p)) ) } \\ Max Alekseyev, Sep 12 2009

Crossrefs

Sequence in context: A171530 A266684 A173683 * A110265 A275415 A021190

Adjacent sequences: A099405 A099406 A099407 * A099409 A099410 A099411

Keyword

nonn

Author

Volker Schmitt (clamsi(AT)gmx.net), Nov 17 2004

Extensions

More terms from Max Alekseyev, Sep 12 2009

Status

approved