A098438 Numbers k such that (30^k - 1)/29 is prime.

2, 5, 11, 163, 569, 1789, 8447, 72871, 78857, 82883

Offset: 1

Author

Tim Honeywill, Jon Ingram, and Paul Boddington, Oct 26 2004

Keywords

• nonn
• more

Comments

No other terms < 10^5. - Robert Price

Links

• H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
• H. Lifchitz, Mersenne and Fermat primes field
• Index to primes in various ranges, form ((k+1)^n-1)/k

Crossrefs

Searching in the OEIS for 'repunit' gives many similar sequences.

Programs

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;

Mathematica

Do[If[PrimeQ[(30^n - 1)/29], Print[n]], {n, 1, 10000}] (* Ryan Propper, Jun 25 2005 *)
Select[Prime[Range[100]],PrimeQ[(30^#-1)/29]&] (* Alexander Adamchuk, Feb 11 2007 *)

PARI

is(n)=n=(30^n-1)/29;denominator(n)==1&&ispseudoprime(n) \\ Charles R Greathouse IV, Jul 01 2013

Extensions

a(5)-a(7), corresponding to probable primes, from Ryan Propper, Jun 25 2005

a(7) = 8447 was found by Richard Fischer in 2004. - Alexander Adamchuk, Feb 11 2007

Edited by N. J. A. Sloane Jan 25 2008 at the suggestion of Herman Jamke (hermanjamke(AT)fastmail.fm)

Edited by T. D. Noe, Oct 30 2008

a(8)-a(10) from Robert Price, Dec 10 2011