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

1,1

Comments

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

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

Example

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

Crossrefs

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

Sequence in context: A297488 A177816 A130653 * A125041 A013806 A147671

Adjacent sequences: A125036 A125037 A125038 * A125040 A125041 A125042

Keyword

nonn

Author

Nick Hobson, Nov 18 2006

Extensions

More terms from Sean A. Irvine, Apr 09 2015

Status

approved