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%I #56 Apr 11 2024 17:22:41
%S 2,19,5,67,7,281,1051,6791,11,115599457,365705201,79352440891,
%T 286351937491,5810592517241,17
%N a(n) is the least prime p such that p + 6*k*(k+1) is prime for 0 <= k <= n-1 but not for k=n.
%C a(10), ..., a(14) > 10^7, a(15) = 17, a(16), ..., a(20) > 10^7.
%C a(29) = 31. - _Chai Wah Wu_, Apr 10 2024
%p f:= proc(p) local k;
%p for k from 1 while isprime(p+k*(k+1)*6) do od:
%p k
%p end proc:
%p A:= Vector(12): count:= 0:
%p for i from 1 while count < 12 do
%p v:= f(ithprime(i));
%p if A[v] = 0 then count:= count+1; A[v]:= ithprime(i) fi
%p od:
%p convert(A,list);
%t Table[p=1;m=6;Monitor[Parallelize[While[True,If[And[MemberQ[PrimeQ[Table[p+m*k*(k+1),{k,0,n-1}]],False]==False,PrimeQ[p+m*n*(n+1)]==False],Break[]];p++];p],p],{n,1,10}]
%o (PARI) isok(p, n) = for (k=0, n-1, if (! isprime(p + 6*k*(k+1)), return(0))); return (!isprime(p + 6*n*(n+1)));
%o a(n) = my(p=2); while (!isok(p, n), p=nextprime(p+1)); p;
%Y Cf. A164926, A371024.
%K nonn,more
%O 1,1
%A _J.W.L. (Jan) Eerland_, Mar 12 2024
%E a(10)-a(11) from _Chai Wah Wu_, Apr 10 2024
%E a(12) from _Chai Wah Wu_, Apr 11 2024
%E a(13)-a(14) from _David A. Corneth_, Apr 11 2024
%E a(15) from _J.W.L. (Jan) Eerland_, Mar 12 2024
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