cp's OEIS Frontend

A204592 Primes p such that (p+1)/2, (p+2)/3, (p+3)/4 and (p+4)/5 are also prime.

%I A204592 #14 Apr 05 2017 17:40:02
%S A204592 19441,266401,423481,539401,600601,663601,908041,1113961,1338241,
%T A204592 1483561,1657441,1673401,2578801,3109681,3150841,3336601,3613681,
%U A204592 4112761,4160641,4798081,5114881,5412961,5516281,5590201,5839681,6078361,7660801,8628481,9362641,9388801,9584401,9733081
%N A204592 Primes p such that (p+1)/2, (p+2)/3, (p+3)/4 and (p+4)/5 are also prime.
%C A204592 Equivalently, primes p in A163573 such that p+4 is a semiprime. (Since all p in A163573 are of the form p=120k+1, p+4 is necessarily a multiple of 5. The other prime factor is then (p+4)/5 = 24k+1.)
%H A204592 Charles R Greathouse IV, <a href="/A204592/b204592.txt">Table of n, a(n) for n = 1..10000</a>
%F A204592 A204592 = A163573 intersect A136061.
%t A204592 Select[Prime[Range[700000]],AllTrue[{(#+1)/2,(#+2)/3,(#+3)/4,(#+4)/5},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Apr 05 2017 *)
%o A204592 (PARI) {my(p=1); until(, isprime(p+=120) || next; for( j=2,5, isprime(p\j+1) || next(2)); print1(p","))}
%o A204592 (PARI) forprime(p=2,1e7,if(p%120==1&&isprime((p+1)/2)&&isprime((p+2)/3)&& isprime((p+3)/4)&&isprime((p+4)/5),print1(p", "))) \\ _Charles R Greathouse IV_, Feb 26 2012
%K A204592 nonn
%O A204592 1,1
%A A204592 _M. F. Hasler_, Feb 26 2012