cp's OEIS Frontend

A224627 Prime numbers p such that 2*p^3-1, 2*p*q^2-1, 2*p*r^2-1, and 2*p*s^2-1 are prime numbers.

%I A224627 #17 Apr 22 2013 12:11:17
%S A224627 19460899,86276401,87980803,167646631,300722029,343507111,479516311,
%T A224627 906597943,998757829,1031308249,1112697199,1311383431,1962194053
%N A224627 Prime numbers p such that 2*p^3-1, 2*p*q^2-1, 2*p*r^2-1, and 2*p*s^2-1 are prime numbers.
%C A224627 Subsequence of A224612, p = prime(n) when A224612(n)=1.
%t A224627 Reap[ For[p = 2, p < 2*10^9, p = NextPrime[p], If[PrimeQ[q = 2*p^3 - 1] && PrimeQ[r = 2*p*q^2 - 1] && PrimeQ[s = 2*p*r^2 - 1] && PrimeQ[2*p*s^2 - 1], Print[p]; Sow[p]] ]][[2, 1]] (* _Jean-François Alcover_, Apr 22 2013 *)
%o A224627 (PFGW & SCRIPTIFY)
%o A224627 SCRIPT
%o A224627 DIM n,1
%o A224627 DIM q
%o A224627 DIMS t
%o A224627 OPENFILEOUT myf,a(n).txt
%o A224627 LABEL a
%o A224627 SET n,n+1
%o A224627 SETS t,%d\,;p(n)
%o A224627 SET q,2*p(n)^3-1
%o A224627 PRP q,t
%o A224627 IF ISPRP THEN GOTO b
%o A224627 GOTO a
%o A224627 LABEL b
%o A224627 SET q,2*p(n)*q^2-1
%o A224627 PRP q,t
%o A224627 IF ISPRP THEN GOTO c
%o A224627 GOTO a
%o A224627 LABEL c
%o A224627 SET q,2*p(n)*q^2-1
%o A224627 PRP q,t
%o A224627 IF ISPRP THEN GOTO d
%o A224627 GOTO a
%o A224627 LABEL d
%o A224627 SET q,2*p(n)*q^2-1
%o A224627 PRP q,t
%o A224627 IF ISPRP THEN GOTO e
%o A224627 GOTO a
%o A224627 LABEL e
%o A224627 WRITE t,myf
%o A224627 GOTO a
%Y A224627 Cf. A224612, A224613, A224614, A224626.
%K A224627 nonn
%O A224627 1,1
%A A224627 _Pierre CAMI_, Apr 12 2013
%E A224627 More terms from _Jean-François Alcover_, Apr 22 2013