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A101045 Record size primes in A101044. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 25 09:37 EST 2022. Contains 350565 sequences. (Running on oeis4.)