A189240 Least number k such that 2*k*n + 1 is a prime dividing 3^n + 1.

1, 1, 5, 6, 6, 39, 1, 1, 59, 3, 270, 15330, 1, 1, 672605, 3, 2, 75, 1, 1, 125, 511647711, 2, 3, 1, 360, 7691, 9, 796056, 111, 14476720225405, 1, 14064, 5355114024, 90, 249, 69757, 1, 180

Offset: 2

Author

Michel Lagneau, Apr 19 2011

Keywords

• nonn

Comments

The smallest prime factor of 3^n+1 of the form 2k*n+1 is A189241(n).

Examples

			a(4) = 5 because 3^4+1 = 2*41 => the smallest prime divisor of the form  2k*n+1 is 41 = 2*5*4+1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 2..658

Crossrefs

Cf. A189241, A074476 (largest prime factor of 3^n + 1)

Programs

Mathematica

Table[p=First/@FactorInteger[3^n+1]; (Select[p, Mod[#1, n] == 1 &, 1][[1]]
  - 1)/(2n), {n, 2, 40}]

PARI

a(n)=forstep(K=2*n+1,3^n+1,2*n,if(Mod(3,K)^n==0,return((k-1)/2/n))) \\ Charles R Greathouse IV, May 15 2013