

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.


2



17, 1336337, 4261668267710686591310687815697, 41, 4390937134822286389262585915435960722186022220433, 241, 1553, 243537789182873, 97, 27673, 4289, 457, 137201, 73, 337, 569891669978849, 617, 1697, 65089, 1609, 761
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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, SpringerVerlag, NY, (1998), p. 271.


LINKS

Sean A. Irvine, Table of n, a(n) for n = 1..29
N. Hobson, Home page (listed in lieu of email address)


EXAMPLE

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


CROSSREFS

Cf. A000945, A007519, A057204A057208, A051308A051335, A124984A124993, A125037A125045.
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



