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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.

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A159687 Number of strong primes < 10^n.

Original entry on oeis.org

0, 10, 73, 574, 4543, 37723, 320991, 2796946, 24758534, 222126290, 2014200162, 18425778658
Offset: 1

Views

Author

Cino Hilliard, Apr 19 2009

Keywords

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.

Examples

			a(2) = 10 because there are 10 strong primes < 10^2: 11, 17, 29, 37, 41, 59, 67, 71, 79, and 97.

Links

Crossrefs

Cf. A051634, A159686.

Programs

  • 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

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
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