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

1,1

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

Table of n, a(n) for n=1..51.

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]

Prog

(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

Crossrefs

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

Sequence in context: A332088 A194955 A217884 * A114847 A171969 A075580

Adjacent sequences: A101042 A101043 A101044 * A101046 A101047 A101048

Keyword

nonn

Author

Jens Kruse Andersen, Nov 28 2004

Status

approved