A361823 a(1) = 3; thereafter, a(n+1) is the smallest prime p such that p - prevprime(p) >= a(n) - prevprime(a(n)).

3, 5, 7, 11, 17, 23, 29, 37, 53, 59, 67, 79, 89, 97, 127, 307, 331, 541, 907, 1151, 1361, 8501, 9587, 12889, 14143, 15727, 19661, 25523, 31469, 156007, 338119, 360749, 370373, 492227, 1349651, 1357333, 1562051, 2010881, 4652507, 11114087, 15204131, 17051887

Offset: 1

Author

Ya-Ping Lu, Mar 25 2023

Keywords

• nonn

Comments

a(n) is the leading prime in the (n+1)-th prime sublist defined in A348178.

Crossrefs

Cf. A001223, A070866, A134266, A348178.

Programs

PARI

a361823(upto) = {my(pp=2, gap=1); forprime (p=3, upto, my(g=p-pp);if(g>=gap, print1(p,", "); gap=g); pp=p)};
a361823(20000000) \\ Hugo Pfoertner, Apr 03 2023

Python

from sympy import nextprime; q = 2; g = 0
while q < 20000000:
    p = nextprime(q); d = p - q
    if d >= g: print(p, end = ', '); g = d
    q = p

Formula

a(n) = nextprime(A134266(n)). - Michel Marcus, Mar 30 2023