cp's OEIS Frontend

A224492 Smallest k such that k*2*p(n)^2-1=q is prime, k*2*q^2-1=r, k*2*r^2-1=s, k*2*r^2-1=t, r, s, and t are also prime.

%I A224492 #23 Apr 12 2013 08:25:55
%S A224492 5103,36189,7315,29608,128115,3496,64590,143079,83919,5586,13209,2833,
%T A224492 235339,61621,164349,2668,84574,1140,47335,108079,7978,181366,146140,
%U A224492 2616,165864,86100,11455,8925,23191,197938,28194,229309,196236,274186
%N A224492 Smallest k such that k*2*p(n)^2-1=q is prime, k*2*q^2-1=r, k*2*r^2-1=s, k*2*r^2-1=t, r, s, and t are also prime.
%C A224492 conjecture: a(n) exist for all n
%C A224492 t=k*2*(k*2*(k*2*(k*2*p(n)^2-1)^2-1)^2-1)^2-1
%C A224492 s=k*2*(k*2*(k*2*p(n)^2-1)^2-1)^2-1
%C A224492 r=k*2*(k*2*p(n)^2-1)^2-1
%C A224492 q=k*2*p(n)^2-1
%H A224492 Pierre CAMI, <a href="/A224492/b224492.txt">Table of n, a(n) for n = 1..80</a>
%t A224492 a[n_] := For[k = 1, True, k++, p = Prime[n]; If[PrimeQ[q = k*2*p^2 - 1] && PrimeQ[r = k*2*q^2 - 1] && PrimeQ[s = k*2*r^2 - 1] && PrimeQ[k*2*s^2 - 1], Return[k]]]; Table[Print[an = a[n]]; an, {n, 1, 34}] (* _Jean-François Alcover_, Apr 12 2013 *)
%o A224492 (PFGW & SCRIPTIFY)
%o A224492 SCRIPT
%o A224492 DIM k
%o A224492 DIM i,0
%o A224492 DIM q
%o A224492 DIMS t
%o A224492 OPENFILEOUT myf,a(n).txt
%o A224492 LABEL a
%o A224492 SET i,i+1
%o A224492 IF i>34 THEN END
%o A224492 SET k,0
%o A224492 LABEL b
%o A224492 SET k,k+1
%o A224492 SETS t,%d,%d,%d\,;k;i;p(i)
%o A224492 SET q,k*2*p(i)^2-1
%o A224492 PRP q,t
%o A224492 IF ISPRP THEN GOTO c
%o A224492 GOTO b
%o A224492 LABEL c
%o A224492 SET q,k*2*q^2-1
%o A224492 PRP q,t
%o A224492 IF ISPRP THEN GOTO d
%o A224492 GOTO b
%o A224492 LABEL d
%o A224492 SET q,k*2*q^2-1
%o A224492 PRP q,t
%o A224492 IF ISPRP THEN GOTO e
%o A224492 GOTO b
%o A224492 LABEL e
%o A224492 SET q,k*2*q^2-1
%o A224492 PRP q,t
%o A224492 IF ISPRP THEN WRITE myf,t
%o A224492 IF ISPRP THEN GOTO a
%o A224492 GOTO b
%Y A224492 Cf. A224489, A224490, A224491.
%K A224492 nonn
%O A224492 1,1
%A A224492 _Pierre CAMI_, Apr 08 2013
%E A224492 Typo in name fixed by _Zak Seidov_, Apr 11 2013