A172995 Numbers k such that (3^k + 7)/2 is prime.

1, 3, 7, 75, 191, 395, 891, 2935, 3855, 59887, 125447

Offset

1,2

Comments

The primes are in A172996.

Naturally these numbers are odd since 3^(2*k) + 7 = (8+1)^k + 7 == 0 (mod 8). - Bruno Berselli, Oct 08 2012

For n <= 9, (3^a(n) + 7)/2 has been proved prime using PARI's ECPP; a(10) corresponds to a BPSW PRP. a(11) > 10^5. - Lucas A. Brown, Feb 10 2021

Links

Table of n, a(n) for n=1..11.

Lucas A. Brown, A172995.py

Mathematica

Select[Range[5000], PrimeQ[(3^# + 7) / 2 ]&] (* Vincenzo Librandi, Oct 05 2012 *)

Prog

(PARI) is(n)=ispseudoprime((3^n+7)/2) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

Sequence in context: A191485 A119572 A362651 * A325476 A234536 A103737

Adjacent sequences: A172992 A172993 A172994 * A172996 A172997 A172998

Keyword

nonn,hard,more

Author

Vincenzo Librandi, Feb 07 2010

Extensions

a(7)-(9) from Vincenzo Librandi, Oct 05 2012

a(10) from Lucas A. Brown, Feb 10 2021

a(11) from Michael S. Branicky, Sep 07 2024

Status

approved