A161897 Prime numbers p for which k = (3^p - 3 * 3^((p + 1) / 2) - 6p + 6) / (3p^2 - 3p) is an integer.

11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459, 2579, 2819, 2879, 2903, 2963, 2999

Offset: 1

Author

Reikku Kulon, Jun 21 2009

Keywords

• easy
• nonn

Comments

Superset of the inverse Sophie Germain primes (A005385): (p - 1) / 2 is almost always prime.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A161896, A000040, A005385, A158034, A158035, A158036, A145918.

Programs

Maple

filter:= p -> isprime(p) and
   (3&^p - 3 * 3&^((p + 1) / 2) - 6*p + 6) mod (3*p^2-3*p) = 0:
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Mar 31 2017