A159686 - OEIS

%I #12 Jul 02 2024 07:19:19

%S 0,508,33551,2751328,216056493,18084221125,1548424793743,

%T 135655041210402,12054551765023934,1084635554912125542,

%U 98583402030663969332,9035771475185456034956

%N Sum 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). For 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 The strong primes < 10^2 are 11, 17, 29, 37, 41, 59, 67, 71, 79, 97. These add up to 508 which is the second term in the sequence.

%o (PARI) lista(pmax) = {my(s = 0, pow = 10, p1 = 2, p2 = 3); forprime(p3 = 5, pmax, if(p2 > pow,print1(s, ", "); pow *= 10); if(2*p2 > p1+p3, s += p2); p1 = p2; p2 = p3);} \\ _Amiram Eldar_, Jul 02 2024

%Y Cf. A051634, A159687.

%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)-a(12) from _Amiram Eldar_, Jul 02 2024