A125040 Primes of the form 16k+1 generated recursively. Initial prime is 17. General term is a(n)=Min {p is prime; p divides (2Q)^8 + 1}, where Q is the product of previous terms in the sequence.

17, 47441, 5136468762577, 1217, 2413992194819190142614641, 113, 52654897, 241, 5310928841473, 673

Offset: 1

Author

Nick Hobson, Nov 18 2006

Keywords

• more
• nonn

Comments

All prime divisors of (2Q)^8 + 1 are congruent to 1 modulo 16.

Examples

			a(3) = 5136468762577 is the smallest prime divisor of (2Q)^8 + 1 = 45820731194492299767895461612240999140120699535617 = 5136468762577 * 33000748370307713 * 270317134666005456817, where Q = 17 * 47441.
		

References

• G. A. Jones and J. M. Jones, Elementary Number Theory, Springer-Verlag, NY, (1998), p. 271.

Crossrefs

Cf. A000945, A094407, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

Programs

Mathematica

a = {17}; q = 1;
For[n = 2, n <= 3, n++,
    q = q*Last[a];
    AppendTo[a, Min[Select[FactorInteger[(2*q)^8 + 1][[All, 1]],
    Mod[#, 16] == 1 &]]];
    ];
a (* Robert Price, Jul 14 2015 *)

Extensions

a(5)-a(10) from Max Alekseyev, Oct 18 2008