A159686 Sum of strong primes < 10^n.

0, 508, 33551, 2751328, 216056493, 18084221125, 1548424793743, 135655041210402, 12054551765023934, 1084635554912125542, 98583402030663969332, 9035771475185456034956

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). For 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

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.

Prog

(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

Crossrefs

Cf. A051634, A159687.

Sequence in context: A152524 A236004 A024019 * A198195 A142819 A183058

Adjacent sequences: A159683 A159684 A159685 * A159687 A159688 A159689

Keyword

nonn,more

Author

Cino Hilliard, Apr 19 2009

Extensions

Edited by N. J. A. Sloane, Apr 20 2009

a(11)-a(12) from Amiram Eldar, Jul 02 2024

Status

approved