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