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

2,3

Comments

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

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A201326 A232247 A200110 * A081820 A306324 A214681

Adjacent sequences: A189237 A189238 A189239 * A189241 A189242 A189243

Keyword

nonn

Author

Michel Lagneau, Apr 19 2011

Status

approved