A125041 Primes of the form 24k+17 generated recursively. Initial prime is 17. General term is a(n) = Min {p is prime; p divides (2Q)^4 + 1; p == 17 (mod 24)}, where Q is the product of previous terms in the sequence.

17, 1336337, 4261668267710686591310687815697, 41, 904641301321079897900944986453955254215268639579197293450763646548520041534444726724543203327659858344185865089, 3449, 18701609, 8009, 38599161306788868932168755721, 857, 130073, 1433, 113, 809, 18954775793

Offset

1,1

Comments

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

At least one prime divisor of (2Q)^4 + 1 is congruent to 2 modulo 3 and hence to 17 modulo 24.

The first four terms are the same as those of A125039.

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..20

Example

a(3) = 4261668267710686591310687815697 is the smallest prime divisor congruent to 17 mod 24 of (2Q)^4 + 1 = 4261668267710686591310687815697, where Q = 17 * 1336337.

Crossrefs

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

Sequence in context: A177816 A130653 A125039 * A013806 A147671 A104536

Adjacent sequences: A125038 A125039 A125040 * A125042 A125043 A125044

Keyword

nonn

Author

Nick Hobson, Nov 18 2006

Extensions

More terms from Sean A. Irvine, Jun 09 2015

Status

approved