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%I #12 Apr 22 2013 12:05:34
%S 29952,12063,1463,6102,11661,49552,639179,2099290,291248,393186,
%T 545251,321303,436641,278295,746832,237852,56490,165901,152847,619755,
%U 777177,3410085,117513,2015421
%N Let p = prime(n). Smallest j such that j*2*p^3-1, j*p*2*q^2-1, j*p*2*r^2-1, and j*p*2*s^2-1 are prime numbers.
%C Conjecture: a(n) exists for all n.
%t a[n_] := For[j = 1, j < 10^7, j++, p = Prime[n]; If[PrimeQ[q = j*2*p^3 - 1] && PrimeQ[r = j*2*p*q^2 - 1] && PrimeQ[s = j*2*p*r^2 - 1] && PrimeQ[j*2*p*s^2 - 1], Return[j]]]; Table[Print[an = a[n]]; an, {n, 1, 24}] (* _Jean-François Alcover_, Apr 12 2013 *)
%Y Cf. A224492, A224609, A224610, A224611.
%K nonn
%O 1,1
%A _Pierre CAMI_, Apr 12 2013
%E More terms from _Jean-François Alcover_, Apr 12 2013
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