A191546 Smallest prime factor of prime(n)^n + 1 having the form 2*k*n+1.

3, 5, 7, 1201, 13421, 28393, 22796593, 15073, 163, 421, 757241, 3512477579761, 79, 29, 24317675453761, 136593761, 21199857783625129028395239857, 37, 2494605276120959, 41, 43, 89, 691, 97, 488700001, 53, 17713, 4201, 59, 181, 2729, 449, 67, 137, 71

Offset: 1

Author

Michel Lagneau, Jun 05 2011

Keywords

• nonn

Examples

			a(4) = 1201 because prime(4)^4 + 1 = 7^4+1 = 2402 = 2*1201; the prime divisor of the form 2kn + 1 is 1201 = 2*150*4 + 1 with k = 150.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..82

Crossrefs

Cf. A069463 (Greatest prime factor of prime(n)^n+1).

Programs

Maple

A191546 := proc(n) local ifs,twkn ; ifs := sort(convert(numtheory[factorset]( 1+ithprime(n)^n),list)) ; for twkn in ifs do if (twkn-1) mod (2*n) = 0 then return twkn; end if; end do: return -1 ; end proc: # R. J. Mathar, Jun 18 2011

Mathematica

Table[p = First /@ FactorInteger[Prime[n]^n + 1]; Select[p, Mod[#1, n] ==
  1 &, 1][[1]], {n, 1, 35}]