%I #21 Apr 09 2024 22:00:29
%S 6,7,9,11,15,21,23,27,33,35,47,77,83,143,167,227,437
%N Numbers m such that m - 4*k^2 is a prime for all k > 0 with k^2 < m/4.
%C No other terms with m < 1000000. - _Colin Barker_, Apr 14 2014
%C If it exists, a(18) > 10^9. - _Jon E. Schoenfield_, Mar 17 2024
%e 21 is in this sequence because 21 - 4*1^2 = 17 and 21 - 4*2^2 = 5 are both prime.
%t n=6;Monitor[Parallelize[While[True,If[MemberQ[PrimeQ[Table[n-4*k^2,{k,1,Floor[Sqrt[n/4]]}]],False]==False,Print[n]];n++];n],n] (* _J.W.L. (Jan) Eerland_, Mar 17 2024 *)
%o (PARI) isOK(n) = k=1; until(k^2>=n/4, if(!isprime(n-4*k^2), return(0)); k++); 1;
%o for(n=3, 1000000, if(isOK(n), print1(n, ", "))) \\ _Colin Barker_, Apr 14 2014
%Y Cf. A240842.
%K nonn,more
%O 1,1
%A _Ilya Lopatin_ and _Juri-Stepan Gerasimov_, Apr 14 2014
%E One missing term and one additional term from _Colin Barker_, Apr 14 2014