A005541 Numbers k such that 8*3^k - 1 is prime.

0, 1, 2, 4, 10, 17, 50, 170, 184, 194, 209, 641, 1298, 4034, 5956, 7154, 9970, 35956, 42730, 132004, 190610

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard

Comments

a(22) > 2*10^5. - Robert Price, Mar 16 2014

All terms are verified primes (i.e., not probable primes). - Robert Price, Mar 16 2014

896701 is a term, found in 2010 (see link). - Jeppe Stig Nielsen, Jul 31 2020

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• The Prime Pages, 8*3^896701 - 1.
• H. C. Williams and C. R. Zarnke, Some prime numbers of the forms 2*3^n+1 and 2*3^n-1, Math. Comp., 26 (1972), 995-998.

Crossrefs

Cf. A003307, A002235, A046865, A079906, A046866, A001771, A056725, A046867, A079907.

Programs

Mathematica

lst={};Do[If[PrimeQ[8*3^n-1], AppendTo[lst, n]], {n, 13^3}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 08 2008 *)

PARI

is(n)=isprime(8*3^n-1) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

More terms from Douglas Burke (dburke(AT)nevada.edu)

0 prepended by Vincenzo Librandi, Sep 26 2012

a(18)-a(21) from Robert Price, Mar 16 2014