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

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

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Last modified June 4 08:49 EDT 2020. Contains 334825 sequences. (Running on oeis4.)