A159687 Number of strong primes < 10^n.

0, 10, 73, 574, 4543, 37723, 320991, 2796946, 24758534, 222126290, 2014200162, 18425778658

Offset: 1

Author

Cino Hilliard, Apr 19 2009

Keywords

• nonn
• more

Comments

Given 3 consecutive primes p1, p2, and p3, p2 is a strong prime if p2 > (p1+p2)/2.

Or, primes that are greater than the arithmetic mean of their immediate surrounding primes.

The number of strong primes < n ~ sum of strong primes < sqrt(n). The number of strong primes < 10^11 = 2014200162 and the sum of strong primes < 10^5.5 = 1972716560, for an error of 0.0206.

Examples

			a(2) = 10 because there are 10 strong primes < 10^2: 11, 17, 29, 37, 41, 59, 67, 71, 79, and 97.
		

Links

• Cino Hilliard, Sum of Strong Primes. [broken link]

Crossrefs

Cf. A051634, A159686.

Programs

Other

See the link for Gcc programs that count and sum these primes.

PARI

lista(pmax) = {my(c = 0, pow = 10, p1 = 2, p2 = 3); forprime(p3 = 5, pmax, if(p2 > pow,print1(c, ", "); pow *= 10); if(2*p2 > p1+p3, c++); p1 = p2; p2 = p3);} \\ Amiram Eldar, Jul 02 2024

Extensions

Edited by N. J. A. Sloane, Apr 20 2009

a(11) corrected by Bill McEachen, Oct 18 2023

a(12) from Amiram Eldar, Jul 02 2024