OFFSET
1,2
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.
LINKS
Cino Hilliard, Sum of Strong Primes. [broken link]
EXAMPLE
a(2) = 10 because there are 10 strong primes < 10^2: 11, 17, 29, 37, 41, 59, 67, 71, 79, and 97.
PROG
(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
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Cino Hilliard, Apr 19 2009
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
STATUS
approved