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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
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
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
KEYWORD
nonn
AUTHOR
Jens Kruse Andersen, Nov 28 2004
STATUS
approved