A034914 Odd primes p such that q=(k*p+1)/(p-k) is prime for some k.

3, 7, 13, 17, 23, 31, 41, 43, 47, 53, 67, 73, 79, 83, 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, 509, 541, 557, 577, 593, 599, 613, 617, 643, 653, 677, 691, 727, 733, 769

Offset

1,1

Comments

Related to hyperperfect numbers of a certain form.

Links

Robert Israel, 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

7 and 43 are both terms since (6*7+1)/(7-6) = 43.

Maple

filter:= proc(p) local g, m, q;
  if not isprime(p) then return false fi;
  g:= p^2+1;
  for m in select(`<`, numtheory:-divisors(g), p) do
     q:= g/m-p;
     if isprime(q) then return true fi;
  od;
  false
end proc:
select(filter, [seq(i, i=3..1000, 2)]); # Robert Israel, Oct 06 2020

Prog

(PARI) isok(p) = {for (k=1, p-1, my(q = (k*p+1)/(p-k)); if ((denominator(q)==1) && isprime(q), return (1)); ); }
lista(nn) = {forprime(p=3, nn, if (isok(p), print1(p, ", ")); ); } \\ Michel Marcus, Mar 11 2016

Crossrefs

Cf. A034913.

Sequence in context: A288709 A040106 A191028 * A034913 A040148 A097957

Adjacent sequences: A034911 A034912 A034913 * A034915 A034916 A034917

Keyword

nonn

Author

Jud McCranie

Extensions

Name edited by Michel Marcus, Mar 11 2016

Status

approved