A125043 - OEIS

A125043

Primes of the form 18k+1 generated recursively. Initial prime is 19. General term is a(n) = Min {p is prime; p divides (R^9 - 1)/(R^3 - 1); p == 1 (mod 9)}, where Q is the product of previous terms in the sequence and R = 3*Q.

19, 20593, 163, 8321800321246060993879, 9002496685879, 9736549840211105800055992105260095004185761, 1117, 48871, 37, 109, 2072647, 811, 2647, 22934467, 73, 10715232331, 4861, 127, 883, 699733, 19918378819555761579853986597710971

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OFFSET

1,1

COMMENTS

All prime divisors of (R^9 - 1)/(R^3 - 1) different from 3 are congruent to 1 modulo 18.

REFERENCES

M. Ram Murty, Problems in Analytic Number Theory, Springer-Verlag, NY, (2001), p. 209.

LINKS

Table of n, a(n) for n=1..21.

EXAMPLE

a(3) = 163 is the smallest prime divisor congruent to 1 mod 18 of (R^9-1)/(R^3-1) = 2615573032645879161713714169238484203 = 163 * 88080931 * 161773561 * 1126133310262611691, where Q = 19 * 20593 and R = 3*Q.

CROSSREFS

Cf. A000945, A061237, A057204-A057208, A051308-A051335, A124984-A124993, A125037-A125045.

Sequence in context: A107100 A233233 A203581 * A249907 A233105 A013528

Adjacent sequences: A125040 A125041 A125042 * A125044 A125045 A125046

KEYWORD

more,nonn

AUTHOR

Nick Hobson, Nov 18 2006

EXTENSIONS

More terms from Sean A. Irvine, Feb 02 2012

STATUS

approved