|
%I #25 Jul 02 2024 07:19:23
%S 0,10,73,574,4543,37723,320991,2796946,24758534,222126290,2014200162,
%T 18425778658
%N Number of strong primes < 10^n.
%C Given 3 consecutive primes p1, p2, and p3, p2 is a strong prime if p2 > (p1+p2)/2.
%C Or, primes that are greater than the arithmetic mean of their immediate surrounding primes.
%C 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.
%H Cino Hilliard, <a href="http://groups.google.com/group/sumprimes/web/count-and-sum-strong-primes?msg=sap">Sum of Strong Primes</a>. [broken link]
%e a(2) = 10 because there are 10 strong primes < 10^2: 11, 17, 29, 37, 41, 59, 67, 71, 79, and 97.
%o (Other) See the link for Gcc programs that count and sum these primes.
%o (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
%Y Cf. A051634, A159686.
%K nonn,more
%O 1,2
%A _Cino Hilliard_, Apr 19 2009
%E Edited by _N. J. A. Sloane_, Apr 20 2009
%E a(11) corrected by _Bill McEachen_, Oct 18 2023
%E a(12) from _Amiram Eldar_, Jul 02 2024
|
