A159687 Number of strong primes < 10^n.

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

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

Table of n, a(n) for n=1..12.

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

Cf. A051634, A159686.

Sequence in context: A200580 A181678 A206817 * A199556 A044197 A044578

Adjacent sequences: A159684 A159685 A159686 * A159688 A159689 A159690

Keyword

nonn,more,changed

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