A034913 Odd primes p such that q = (k*p+1)/(p-k) is prime for some p/2 < k < p.

3, 7, 13, 17, 23, 31, 47, 53, 67, 73, 79, 113, 137, 139, 151, 157, 163, 173, 193, 227, 257, 293, 307, 317, 337, 349, 353, 379, 401, 419, 457, 463, 467, 479, 487, 499, 541, 557, 577, 593, 599, 613, 617, 643, 653, 677, 691, 727, 733, 769, 787, 811, 829, 853

Offset

1,1

Comments

Related to hyperperfect numbers of a certain form.

Old name was: Primes such that q=(k*a(n)+1)/(a(n)-k), is prime for some k, q>a(n).

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

J. S. McCranie, A study of hyperperfect numbers, J. Int. Seqs. Vol. 3 (2000) #P00.1.3.

Example

137 is a term since (132*137+1)/(137-132) = 3617 is prime.

Prog

(PARI) isok(p)=for (k=1, p-1, my(q = (k*p+1)/(p-k)); if ((q > p) && (denominator(q)==1) && isprime(q), return (1)); );
lista(nn) = forprime(p=3, nn, if (isok(p), print1(p, ", "))) \\ Michel Marcus, Mar 11 2016
(PARI) is(p)=fordiv(p^2+1, d, if(d>=p/2, return(0)); if(isprime((p*(p-d)+1)/d), return(isprime(p)))) \\ Charles R Greathouse IV, Mar 11 2016

Crossrefs

Cf. A034914.

Sequence in context: A040106 A191028 A034914 * A040148 A097957 A071774

Adjacent sequences: A034910 A034911 A034912 * A034914 A034915 A034916

Keyword

nonn

Author

Jud McCranie

Extensions

Name edited by Michel Marcus and Charles R Greathouse IV, Mar 11 2016

Status

approved