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Numbers m such that m - 4*k^2 is a prime for all k > 0 with k^2 < m/4.
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%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