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A339096 Record values in A306400.

%I A339096 #17 Mar 07 2024 08:52:21
%S A339096 5,7,11,23,701,3989,4397,5501,7309,9281,10331,11243,12907,16127,27917,
%T A339096 39901,43051,44843,48397,66569,70657
%N A339096 Record values in A306400.
%e A339096 a(3) = 11 is in the sequence because A306400(5) = 11 and A306400(k)<11 for k < 5.
%p A339096 g:= proc(p) local q;
%p A339096   q:= 3:
%p A339096   do
%p A339096     q:= nextprime(q);
%p A339096     if isprime(p+q^2-1) and isprime(p+q^2+1) then return q fi;
%p A339096   od
%p A339096 end proc:
%p A339096 R:= NULL: count:= 0: w:= 0:
%p A339096 for nn from 5 by 6 while count < 15 do
%p A339096   if isprime(nn) then
%p A339096     v:= g(nn);
%p A339096     if v > w then count:= count+1; R:= R, v; w:= v; fi
%p A339096     fi
%p A339096 od:
%p A339096 R;
%t A339096 g[p_] := Module[{q}, q = 3; While[True, q = NextPrime[q]; If [PrimeQ[p + q^2 - 1] && PrimeQ[p + q^2 + 1], Return@q]]];
%t A339096 R = {}; count = 0; w = 0;
%t A339096 For[nn = 5, count < 15, nn = nn + 6, If[PrimeQ[nn], v = g[nn]; If[v > w, count++; Print[count, " ", v]; R = Append[R, v]; w = v]]];
%t A339096 R (* _Jean-François Alcover_, Mar 07 2024, after _Robert Israel_ *)
%Y A339096 Cf. A306400.
%K A339096 nonn,more
%O A339096 1,1
%A A339096 _Robert Israel_, Nov 23 2020
%E A339096 a(16)-a(17) from _Jinyuan Wang_, Dec 04 2020
%E A339096 a(18)-a(21) from _Chai Wah Wu_, Jan 15 2021