

A125042


Primes of the form 48k+17 generated recursively. Initial prime is 17. General term is a(n)=Min {p is prime; p divides (2Q)^8 + 1; Mod[p,48]=17}, where Q is the product of previous terms in the sequence.


0




OFFSET

1,1


COMMENTS

All prime divisors of (2Q)^8 + 1 are congruent to 1 modulo 16.
At least one prime divisor of (2Q)^8 + 1 is congruent to 2 modulo 3 and hence to 17 modulo 48.
The first two terms are the same as those of A125040.


REFERENCES

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


LINKS

Table of n, a(n) for n=1..4.
N. Hobson, Home page (listed in lieu of email address)


EXAMPLE

a(3) = 33000748370307713 is the smallest prime divisor congruent to 17 mod 48 of (2Q)^8 + 1 = 45820731194492299767895461612240999140120699535617 = 5136468762577 * 33000748370307713 * 270317134666005456817, where Q = 17 * 47441.


MATHEMATICA

a = {17}; q = 1;
For[n = 2, n ≤ 2, n++,
q = q*Last[a];
AppendTo[a, Min[Select[FactorInteger[(2*q)^8 + 1][[All, 1]],
Mod[#, 48] \[Equal] 17 &]]];
];
a (* Robert Price, Jul 14 2015 *)


CROSSREFS

Cf. A000945, A057204A057208, A051308A051335, A124984A124993, A125037A125045.
Sequence in context: A068733 A066161 A125040 * A138942 A075902 A013760
Adjacent sequences: A125039 A125040 A125041 * A125043 A125044 A125045


KEYWORD

more,nonn


AUTHOR

Nick Hobson, Nov 18 2006


STATUS

approved



