A319228 Number of primes of the form b^2 + b + 1 for b <= 10^n.

6, 32, 189, 1410, 10751, 88118, 745582, 6456835, 56988601, 510007598, 4615215645

Offset: 1

Author

Seiichi Manyama, Sep 14 2018

Keywords

• nonn
• more

Examples

			a(1) = 6 because there are 6 primes of the form b^2 + b + 1 for b <= 10: 3, 7, 13, 31, 43 and 73.
		

Crossrefs

Cf. A002383, A002384, A206709.

Programs

PARI

{a(n) = sum(k=0, 10^n, isprime(k^2+k+1))}

Python

from sympy import isprime
def A319228(n):
    c, b, b2, n10 = 0, 1, 3, 10**n
    while b <= n10:
        if isprime(b2):
            c += 1
        b += 1
        b2 += 2*b
    return c # Chai Wah Wu, Sep 17 2018

Extensions

a(10) from Chai Wah Wu, Sep 17 2018

a(11) from Chai Wah Wu, Sep 18 2018