A134266 Primes associated with the prime gaps listed in A085237.

2, 3, 5, 7, 13, 19, 23, 31, 47, 53, 61, 73, 83, 89, 113, 293, 317, 523, 887, 1129, 1327, 8467, 9551, 12853, 14107, 15683, 19609, 25471, 31397, 155921, 338033, 360653, 370261, 492113, 1349533, 1357201, 1561919, 2010733, 4652353, 11113933, 15203977, 17051707, 20831323, 47326693, 122164747, 189695659, 191912783

Offset: 1

Author

David W. Wilson, Dec 31 2007

Keywords

• nonn

Comments

The smallest prime p(n) such that p(n+1)-p(n) is nondecreasing. The smallest prime p(n) such that (p(n+1)/p(n))^p(n) is increasing. [Thomas Ordowski, May 26 2012]

a(n) is the last prime in the n-th sublist of prime numbers defined in A348178. - Ya-Ping Lu, Oct 19 2021

Links

• Michel Planat and Patrick Solé, Improving Riemann prime counting, arXiv preprint arXiv:1410.1083 [math.NT], 2014.

Crossrefs

See also A205827(n) = A000040(A214935(n)), A182514(n) = A000040(A241540(n)).

Cf. A348178.

Programs

Python

from sympy import nextprime; p, r = 2, 0
while p < 2*10**8:
    q = nextprime(p); g = q - p
    if g >= r: print(p, end = ', '); r = g
    p = q # Ya-Ping Lu, Jan 23 2024

Formula

a(n) = A000040(A085500(n)). - M. F. Hasler, Apr 26 2014