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%I #36 Dec 11 2022 12:39:40
%S 1,1,1,1,2,3,7,10,18,43,86,185,449,1091,2764,6978,17951,47146,125507,
%T 337600,916229,2504458,6898908
%N Number of primes p of the form k^2 + 1 less than 10^n such that p+2 and 2p+1 are also primes.
%e For n = 5, a(5) = 2 since 5 and 25601 are the only two such primes less than or equal to 10^5.
%t seq[nmax_] := Module[{c = 0, pow = 10, s = {}, p}, Do[p = k^2 + 1; If[PrimeQ[p] && PrimeQ[p + 2] && PrimeQ[2*p + 1], c++]; If[p > pow, pow *= 10; AppendTo[s, c]], {k, 1, Floor[10^(nmax/2)] + 1}]; s]; seq[13] (* _Amiram Eldar_, Oct 16 2022 *)
%Y Cf. A006880, A007508, A083844, A092816, A347934.
%K nonn,more
%O 1,5
%A _Angad Singh_, Oct 16 2022