A191547 a(n) is the smallest number k such that 2*k*n + 1 is a prime dividing prime(n)^n + 1.

1, 1, 1, 150, 1342, 2366, 1628328, 942, 9, 21, 34420, 146353232490, 3, 1, 810589181792, 4268555, 623525228930150853776330584, 1, 65647507266341, 1, 1, 2, 15, 2, 9774000, 1, 328, 75, 1, 3, 44, 7, 1, 2, 1, 1, 3, 16353757, 2, 5036, 1, 23, 23, 1, 216, 1218482865908370401

Offset: 1

Author

Michel Lagneau, Jun 05 2011

Keywords

• nonn

Examples

			a(4) = 150 because 2*150*4 + 1 = 1201, which is the smallest prime of the form 2*k*4 + 1 that divides prime(4)^4 + 1 = 7^4 + 1 = 2402 = 2*1201.
		

Links

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

Crossrefs

Cf. A062006, A191546.

Programs

Maple

A191547 :=proc(n) local d,a,k ; a := -1 ; for d in numtheory[factorset](ithprime(n)^n+1) do k := (d-1)/2/n ; if type(k,'integer') and k >0 then if a = -1 then a := k; elif k < a then a := k; end if; end if ; end do: return a ; end proc: # R. J. Mathar, Jun 08 2011

Mathematica

Table[p=First/@FactorInteger[Prime[ n]^n+1]; (Select[p, Mod[#1, n] == 1 &,
  1][[1]] - 1)/(2n), {n, 1, 35}]

Extensions

a(31)-a(46) from Amiram Eldar, Feb 17 2020