A125039 Primes of the form 8k+1 generated recursively. Initial prime is 17. General term is a(n)=Min {p is prime; p divides (2Q)^4 + 1}, where Q is the product of previous terms in the sequence.

17, 1336337, 4261668267710686591310687815697, 41, 4390937134822286389262585915435960722186022220433, 241, 1553, 243537789182873, 97, 27673, 4289, 457, 137201, 73, 337, 569891669978849, 617, 1697, 65089, 1609, 761

Offset: 1

Author

Nick Hobson, Nov 18 2006

Keywords

• nonn

Comments

All prime divisors of (2Q)^4 + 1 are congruent to 1 modulo 8.

Examples

			a(3) = 4261668267710686591310687815697 is the smallest prime divisor of (2Q)^4 + 1 = 4261668267710686591310687815697, where Q = 17 * 1336337.
		

References

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

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..29

Crossrefs

Cf. A000945, A007519, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

Extensions

More terms from Sean A. Irvine, Apr 09 2015