A216146 Smallest prime factor of 3*(2n+1)^(2n+1) + 2.

5, 83, 9377, 2470631, 97, 5, 29, 13, 306503, 23173, 5, 7, 7, 11, 12517, 5, 13, 61, 17, 71, 5, 53, 1531477446517, 97, 101, 5, 11, 1999, 53, 11, 5, 67153, 7, 7, 13499, 5, 13, 28201

Offset: 0

Author

M. F. Hasler, Sep 02 2012

Keywords

• nonn

Examples

			Indices n = 0,1,2,3 correspond to the 4 primes a(n) = 3*(2n+1)^(2n+1) + 2, and to A160360(2,3,4,5) = 1,3,5,7. The next prime is a(46), with 184 digits too large to be displayed here.
a(22)=1531477446517 is the smaller factor of the semiprime 3*45^45+2.
		

Links

• Factor DB, 3*(2*n+1)^(2*n+1)+2.

Crossrefs

Cf. A160360.

Programs

Mathematica

Table[FactorInteger[3(2n+1)^(2n+1)+2][[1,1]],{n,0,40}] (* Harvey P. Dale, Jan 25 2025 *)

PARI

forstep(n=1,300,2,forprime(p=1,default(primelimit),Mod(n,p)^n*3+2&next;print1(p",");next(2));print1(factor(3*n^n+2)[1,1]","))

Extensions

Comment in example and link added by M. F. Hasler, Feb 03 2014