A125040 - OEIS

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

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OFFSET

1,1

COMMENTS

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

REFERENCES

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

LINKS

Table of n, a(n) for n=1..10.

EXAMPLE

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

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 *)

CROSSREFS

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

Sequence in context: A110915 A068733 A066161 * A125042 A373896 A138942

Adjacent sequences: A125037 A125038 A125039 * A125041 A125042 A125043