A034914 - OEIS

%I #20 Oct 06 2020 14:41:29

%S 3,7,13,17,23,31,41,43,47,53,67,73,79,83,113,137,139,151,157,163,173,

%T 193,227,257,293,307,317,337,349,353,379,401,419,457,463,467,479,487,

%U 499,509,541,557,577,593,599,613,617,643,653,677,691,727,733,769

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

%C Related to hyperperfect numbers of a certain form.

%H Robert Israel, <a href="/A034914/b034914.txt">Table of n, a(n) for n = 1..10000</a>

%H J. S. McCranie, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL3/mccranie.html">A study of hyperperfect numbers</a>, J. Int. Seqs. Vol. 3 (2000) #P00.1.3.

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

%p filter:= proc(p) local g,m,q;

%p   if not isprime(p) then return false fi;

%p   g:= p^2+1;

%p   for m in select(`<`,numtheory:-divisors(g),p) do

%p      q:= g/m-p;

%p      if isprime(q) then return true fi;

%p   od;

%p   false

%p end proc:

%p select(filter, [seq(i,i=3..1000,2)]); # _Robert Israel_, Oct 06 2020

%o (PARI) isok(p) = {for (k=1, p-1, my(q = (k*p+1)/(p-k)); if ((denominator(q)==1) && isprime(q), return (1)););}

%o lista(nn) = {forprime(p=3, nn, if (isok(p), print1(p, ", ")););} \\ _Michel Marcus_, Mar 11 2016

%Y Cf. A034913.

%K nonn

%O 1,1

%A _Jud McCranie_

%E Name edited by _Michel Marcus_, Mar 11 2016