A189241 Smallest prime factor of 3^n+1 having the form 2*k*n+1.

5, 7, 41, 61, 73, 547, 17, 19, 1181, 67, 6481, 398581, 29, 31, 21523361, 103, 73, 2851, 41, 43, 5501, 23535794707, 97, 151, 53, 19441, 430697, 523, 47763361, 6883, 926510094425921, 67, 956353, 374857981681, 6481, 18427, 5301533, 79, 14401

Offset: 2

Author

Michel Lagneau, Apr 19 2011

Keywords

• nonn

Comments

The values of k are in A189240.

Examples

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

Links

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

Crossrefs

Cf. A189240, 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]],
  {n, 2, 40}]