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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
17, 47441, 33000748370307713, 21377 (list; graph; refs; listen; history; text; internal format)
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, Springer-Verlag, 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, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

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

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Last modified February 21 01:03 EST 2020. Contains 332086 sequences. (Running on oeis4.)