A101045 Record size primes in A101044.

2, 3, 5, 7, 13, 19, 31, 43, 53, 67, 79, 101, 149, 157, 163, 181, 197, 227, 307, 349, 379, 409, 431, 619, 631, 661, 691, 751, 757, 811, 829, 1093, 1117, 1217, 1279, 1423, 1453, 1481, 1531, 1549, 1579, 1759, 1877, 2239, 2273, 2287, 2383, 2447, 2659, 2671, 2707

Offset: 1

Author

Jens Kruse Andersen, Nov 28 2004

Keywords

• nonn

Comments

This sequence (except 2) is also the record size primes in the longer A020483.

Conjecture: lim_{n->infinity} a(n)/n^2 = 1. - Ya-Ping Lu, Sep 24 2020

Links

• J. K. Andersen, Prime gaps (not necessarily consecutive).
• Taras Goy and Mark Shattuck, Determinant Formulas of Some Hessenberg Matrices with Jacobsthal Entries, Applications and Appl. Math.: An Int'l J. (2021) Vol. 16, Issue 1, Art. 10.
• Mike Oakes, Ed Pegg Jr, and Jens Kruse Andersen, Prime gaps (not necessarily consecutive), digest of 5 messages in primenumbers Yahoo group, Nov 26 - Nov 27, 2004. [Cached copy]

Crossrefs

Cf. A020483, A101042, A101043, A101044, A101046.

Programs

Python

from sympy import isprime, nextprime
m = p_max = 0
while m >= 0:
    p = 2
    while isprime(p + 2*m) == 0:
        p = nextprime(p)
    if p > p_max:
        print(p)
        p_max = p
    m += 1 # Ya-Ping Lu, Sep 24 2020