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A179625 Legal generalized repunit prime numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 3 10:58 EDT 2022. Contains 357231 sequences. (Running on oeis4.)