A125044 Primes of the form 54k+1 generated recursively. Initial prime is 109. General term is a(n) = Min {p is prime; p divides (R^27 - 1)/(R^9 - 1); p == 1 (mod 27)}, where Q is the product of previous terms in the sequence and R = 3*Q.

109, 50221, 379, 5077, 2527181639419400128997560106426867837203, 112807, 2094067, 1567, 9325207, 370603, 67447, 27978113462777647321591, 1012771, 163, 396577, 7096357, 3511, 3673, 541, 389287, 1999, 68979565009, 649108891

Offset

1,1

Comments

All prime divisors of (R^27 - 1)/(R^9 - 1) different from 3 are congruent to 1 modulo 54.

References

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

Links

Table of n, a(n) for n=1..23.

Example

a(2) = 50221 is the smallest prime divisor congruent to 1 mod 54 of
  (R^27-1)/(R^9- 1) = 1827509098737085519727094436535854935801097657 = 50221 * 106219 * 342587871163695447795790279515751543, where Q = 109 and R = 3*Q.

Crossrefs

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

Sequence in context: A227949 A144930 A190827 * A352466 A096209 A287469

Adjacent sequences: A125041 A125042 A125043 * A125045 A125046 A125047

Keyword

nonn

Author

Nick Hobson, Nov 18 2006

Extensions

More terms from Sean A. Irvine, Dec 11 2011

Status

approved