A302434 Number of primes of the form b^2 + 2 for b <= 10^n.

4, 12, 69, 447, 3423, 27869, 236985, 2054022, 18127693, 162237123

Offset: 1

Author

Seiichi Manyama, Apr 07 2018

Keywords

• nonn
• more

Comments

From Jacques Tramu, Sep 13 2018: (Start)

Table C(i) = a(i)/(n*log(n)), with n = 10^i:

a(1) = 4 C(1) = 0.92103404

a(2) = 12 C(2) = 0.55262042

a(3) = 69 C(3) = 0.47663511

a(4) = 447 C(4) = 0.41170221

a(5) = 3423 C(5) = 0.39408744

a(6) = 27869 C(6) = 0.38502446

a(7) = 236985 C(7) = 0.38197469

a(8) = 2054022 C(8) = 0.37836484

a(9) = 18127693 C(9) = 0.37566500

a(10) = 162237123 C(10) = 0.37356478

(End)

Examples

			a(1) = 4 because there are 4 primes of the form b^2+2 for b <= 10: 2, 3, 11 and 83.
		

Crossrefs

Number of primes of the form b^2+m for b <= 10^n: A302443 (m=-3), A302442 (m=-2), A206709 (m=1), this sequence (m=2), A302435 (m=3).

Cf. A056899.

Programs

PARI

{a(n) = sum(k=0, 10^n, isprime(k^2+2))}

Extensions

a(10) from Jacques Tramu, Sep 13 2018