A034934 Numbers k such that (3*k + 1)/2 is prime.

1, 3, 7, 11, 15, 19, 27, 31, 35, 39, 47, 55, 59, 67, 71, 75, 87, 91, 99, 111, 115, 119, 127, 131, 151, 155, 159, 167, 171, 175, 179, 187, 195, 207, 211, 231, 235, 239, 255, 259, 267, 279, 287, 295, 299, 307, 311, 319, 327, 335, 339, 347, 371, 375, 379, 391

Offset: 1

Author

Jud McCranie

Keywords

• nonn

Comments

Related to hyperperfect numbers of a certain form.

The formula by Jaroslav Krizek is explained as follows: If p = (3n+1)/2 is prime, then it is an integer, and p must be of the form p = 3m-1, i.e., p = A003627(k). On the other hand, if p = A003627(k), then all k < p are coprime to p, so we have B(p) = (Sum_{kM. F. Hasler, Nov 29 2010

Examples

			a(6) = 19 because for A003627(6) = 29, B(29) = A053818(29)/A023896(29) = 7714/406 = 19. Cf. A179871-A179891, A003627, A007645. - _Jaroslav Krizek_, Aug 01 2010
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Judson S. McCranie, A study of hyperperfect numbers, J. Int. Seq., Vol. 3 (2000), Article 00.1.3.

Crossrefs

Cf. A003627, A007645, A038536, A045309, A175505, A179871-A179891.

Programs

Magma

[ n: n in [1..400 by 2] | IsPrime((3*n+1) div 2) ];

Mathematica

Select[Range[500], PrimeQ[(3# + 1)/2] &] (* Harvey P. Dale, Jan 15 2011 *)

PARI

is(n)=isprime((3*n+1)/2) \\ Charles R Greathouse IV, Feb 20 2017

Formula

a(n) = A175505(A003627(n)). - Jaroslav Krizek, Aug 01 2010

Extensions

Corrected by Vincenzo Librandi, Mar 24 2010