This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A159686 #12 Jul 02 2024 07:19:19
%S A159686 0,508,33551,2751328,216056493,18084221125,1548424793743,
%T A159686 135655041210402,12054551765023934,1084635554912125542,
%U A159686 98583402030663969332,9035771475185456034956
%N A159686 Sum of strong primes < 10^n.
%C A159686 Given 3 consecutive primes p1, p2, and p3, p2 is a strong prime if p2 > (p1+p2)/2.
%C A159686 Or, primes that are greater than the arithmetic mean of their immediate surrounding primes.
%C A159686 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 A159686 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 A159686 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 A159686 (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 A159686 Cf. A051634, A159687.
%K A159686 nonn,more
%O A159686 1,2
%A A159686 _Cino Hilliard_, Apr 19 2009
%E A159686 Edited by _N. J. A. Sloane_, Apr 20 2009
%E A159686 a(11)-a(12) from _Amiram Eldar_, Jul 02 2024