A356364 Number of primes p of the form k^2 + 1 less than 10^n such that p+2 and 2p+1 are also primes.

1, 1, 1, 1, 2, 3, 7, 10, 18, 43, 86, 185, 449, 1091, 2764, 6978, 17951, 47146, 125507, 337600, 916229, 2504458, 6898908

Offset: 1

Author

Angad Singh, Oct 16 2022

Keywords

• nonn
• more

Examples

			For n = 5, a(5) = 2 since 5 and 25601 are the only two such primes less than or equal to 10^5.
		

Crossrefs

Cf. A006880, A007508, A083844, A092816, A347934.

Programs

Mathematica

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 *)