A179625 Legal generalized repunit prime numbers.

5, 7, 13, 31, 43, 73, 157, 211, 241, 1093, 2801, 19531, 22621, 30941, 55987, 88741, 245411, 292561, 346201, 797161, 5229043, 8108731, 12207031, 25646167, 305175781, 321272407, 917087137, 16148168401, 2141993519227, 10778947368421, 17513875027111, 610851724137931, 50544702849929377

Offset: 1

Author

Tim Johannes Ohrtmann, Jan 09 2011

Keywords

• nonn

Comments

In Chris Caldwell's sense, a legal generalized repunit prime is a prime number of the form (b^p-1)/(b-1) such that 3 <= b <= 5*p, b != 10, and p prime.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..640, replacing an earlier file of T. D. Noe
• Chris Caldwell, The Top Twenty: Generalized Repunit
• Robert Granger and Andrew Moss, Generalised Mersenne numbers revisited, arXiv:1108.3054 [math.NT], 2011-2012.

Crossrefs

Cf. A076481, A086122, A165210, A102170 (repunit primes in bases 3, 5, 6, and 7)

This sequence except for the term 5 is subsequence of A085104.

Programs

Mathematica

lim=10^17; n=1; Sort[Reap[While[p=Prime[n]; b=3; While[num=Cyclotomic[p,b]; b<=5p && num<=lim, If[b!=10 && PrimeQ[num], Sow[num]]; b++]; b>3, n++]][[2,1]]]

PARI

upTo(lim)=my(v=List(),t);forprime(p=2,log(2*lim+1)\log(3),for(b=3,5*p,if(b==10,next);t=(b^p-1)/(b-1);if(t>lim,break);if(isprime(t),listput(v,t))));vecsort(Vec(v)) \\ Charles R Greathouse IV, Aug 21 2011