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%I #14 Jun 18 2021 14:48:12
%S 30,42,30,84,516,768,804,4806,2838,174,23418,22770
%N Consider the sequence b(0)=127 and for n>0, b(n) is the least prime of the form k * b(n-1)^2 - 1 where k is a multiple of 6. This sequence gives the values of k.
%e 127,
%e 30*127^2-1,
%e 42*(30*127^2-1)^2-1,
%e 30*(42*(30*127^2-1)^2-1)^2-1,
%e 84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1,
%e 516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1,
%e 768*(516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1)^2-1,
%e 804*(768*(516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1,
%e 4806*(804*(768*(516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1,
%e 2838*(4806*(804*(768*(516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1,
%e 174*(2838*(4806*(804*(768*(516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1,
%e 23418*(174*(2838*(4806*(804*(768*(516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1,
%e and 22770*(23418*(174*(2838*(4806*(804*(768*(516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1,
%e are primes.
%t lpf[{n_,t_}]:=Module[{a=t^2,k=6},While[!PrimeQ[k*a-1],k=k+6];{k,k*a-1}]; Rest[ NestList[lpf,{127,127},12][[All,1]]] (* _Harvey P. Dale_, Apr 25 2017 *)
%K nonn,more
%O 1,1
%A _Pierre CAMI_, Sep 17 2005
%E Edited by _Ray Chandler_, Sep 26 2005
%E Definition amended by _Georg Fischer_, Jun 18 2021