

A124993


Primes of the form 22k+1 generated recursively. Initial prime is 23. General term is a(n)=Min {p is prime; p divides (R^11  1)/(R  1); Mod[p,11]=1}, where Q is the product of previous terms in the sequence and R = 11Q.


18



23, 4847239, 2971, 3936923, 9461, 1453, 331, 81373909, 89, 920771904664817214817542307, 353, 401743, 17088192002665532981, 11617
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OFFSET

1,1


COMMENTS

All prime divisors of (R^11  1)/(R  1) different from 11 are congruent to 1 modulo 22.


REFERENCES

M. Ram Murty, Problems in Analytic Number Theory, SpringerVerlag, NY, (2001), pp. 208209.


LINKS

Table of n, a(n) for n=1..14.
N. Hobson, Home page (listed in lieu of email address)


EXAMPLE

a(3) = 2971 is the smallest prime divisor congruent to 1 mod 22 of (R^111)/(R1) =
7693953366218628230903493622259922359469805176129784863956847906415055607909988155588181877
= 2971 * 357405886421 * 914268562437006833738317047149 * 7925221522553970071463867283158786415606996703, where Q = 23 * 4847239, and R = 11Q.


MATHEMATICA

a={23}; q=1;
For[n=2, n<=2, n++,
q=q*Last[a]; r=11*q;
AppendTo[a, Min[Select[FactorInteger[(r^111)/(r1)][[All, 1]], Mod[#, 11]==1 &]]];
];
a (* Robert Price, Jul 14 2015 *)


CROSSREFS

Cf. A000945, A057204A057208, A051308A051335, A124984A124993, A125037A125045.
Sequence in context: A013772 A034247 A050234 * A013818 A087527 A013906
Adjacent sequences: A124990 A124991 A124992 * A124994 A124995 A124996


KEYWORD

more,nonn


AUTHOR

Nick Hobson, Nov 18 2006


EXTENSIONS

More terms from Max Alekseyev, May 29 2009


STATUS

approved



