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

1,1

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.

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]]]

Prog

(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

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.

Sequence in context: A178648 A241859 A293059 * A141191 A101782 A288889

Adjacent sequences: A179622 A179623 A179624 * A179626 A179627 A179628

Keyword

nonn

Author

Tim Johannes Ohrtmann, Jan 09 2011

Status

approved