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%I #35 Sep 08 2022 08:45:15
%S 2,5,11,163,569,1789,8447,72871,78857,82883
%N Numbers k such that (30^k - 1)/29 is prime.
%C No other terms < 10^5. - _Robert Price_
%H H. Dubner, <a href="http://dx.doi.org/10.1090/S0025-5718-1993-1185243-9">Generalized repunit primes</a>, Math. Comp., 61 (1993), 927-930.
%H H. Lifchitz, <a href="http://www.primenumbers.net/Henri/us/MersFermus.htm">Mersenne and Fermat primes field</a>
%H <a href="/index/Pri#primepop">Index to primes in various ranges</a>, form ((k+1)^n-1)/k
%t Do[If[PrimeQ[(30^n - 1)/29], Print[n]], {n, 1, 10000}] (* _Ryan Propper_, Jun 25 2005 *)
%t Select[Prime[Range[100]],PrimeQ[(30^#-1)/29]&] (* _Alexander Adamchuk_, Feb 11 2007 *)
%o (Magma) for i in [1..500] do if i mod 50 eq 0 then print "counter equals", counter; end if; if IsPrime(i) then n := 0; for j in [0..i-1] do n +:= 30^j; end for; if IsPrime(n) then print n; print i; end if; end if; end for;
%o (PARI) is(n)=n=(30^n-1)/29;denominator(n)==1&&ispseudoprime(n) \\ _Charles R Greathouse IV_, Jul 01 2013
%Y Searching in the OEIS for 'repunit' gives many similar sequences.
%K nonn,more
%O 1,1
%A _Tim Honeywill_, Jon Ingram, and _Paul Boddington_, Oct 26 2004
%E a(5)-a(7), corresponding to probable primes, from _Ryan Propper_, Jun 25 2005
%E a(7) = 8447 was found by _Richard Fischer_ in 2004. - _Alexander Adamchuk_, Feb 11 2007
%E Edited by _N. J. A. Sloane_ Jan 25 2008 at the suggestion of Herman Jamke (hermanjamke(AT)fastmail.fm)
%E Edited by _T. D. Noe_, Oct 30 2008
%E a(8)-a(10) from _Robert Price_, Dec 10 2011
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