A302442 Number of primes of the form b^2-2 for b <= 10^n.

5, 26, 157, 1153, 8888, 72928, 615643, 5328644, 47034083, 420950239

Offset: 1

Author

Seiichi Manyama, Apr 08 2018

Keywords

• nonn
• more

Comments

From Jacques Tramu, Sep 13 2018: (Start)

Table C(i) = a(i)/pi(10^i) = a(i)/A000720(10^i)

a(1) = 5 C(1) = 1.25000000

a(2) = 26 C(2) = 1.04000000

a(3) = 157 C(3) = 0.93452381

a(4) = 1153 C(4) = 0.93816111

a(5) = 8888 C(5) = 0.92660550

a(6) = 72928 C(6) = 0.92904278

a(7) = 615643 C(7) = 0.92636541

a(8) = 5328644 C(8) = 0.92487818

a(9) = 47034083 C(9) = 0.92500224

a(10) = 420950239 C(10) = 0.92505860

(End)

Examples

			a(1) = 5 because there are 5 primes of the form b^2-2 for b <= 10 : 2, 7, 23, 47 and 79.
		

Crossrefs

Number of primes of the form b^2+m for b <= 10^n: A302443 (m=-3), this sequence (m=-2), A206709 (m=1), A302434 (m=2), A302435 (m=3).

Cf. A028871.

Programs

PARI

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

Python

from sympy import isprime
def aupton(terms):
  s, alst = 0, []
  for n in range(1, terms+1):
    s += sum(isprime(b**2-2) for b in range(10**(n-1), 10**n))
    alst.append(s)
  return alst
print(aupton(6)) # Michael S. Branicky, May 26 2021

Extensions

a(10) from Jacques Tramu, Sep 14 2018