A101045 - OEIS

%I #21 Sep 28 2021 19:59:13

%S 2,3,5,7,13,19,31,43,53,67,79,101,149,157,163,181,197,227,307,349,379,

%T 409,431,619,631,661,691,751,757,811,829,1093,1117,1217,1279,1423,

%U 1453,1481,1531,1549,1579,1759,1877,2239,2273,2287,2383,2447,2659,2671,2707

%N Record size primes in A101044.

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

%C Conjecture: lim_{n->infinity} a(n)/n^2 = 1. - _Ya-Ping Lu_, Sep 24 2020

%H J. K. Andersen, <a href="http://groups.yahoo.com/group/primenumbers/message/15641">Prime gaps (not necessarily consecutive)</a>.

%H Taras Goy and Mark Shattuck, <a href="https://digitalcommons.pvamu.edu/aam/vol16/iss1/10/">Determinant Formulas of Some Hessenberg Matrices with Jacobsthal Entries</a>, Applications and Appl. Math.: An Int'l J. (2021) Vol. 16, Issue 1, Art. 10.

%H Mike Oakes, Ed Pegg Jr, and Jens Kruse Andersen, <a href="/A101042/a101042.txt">Prime gaps (not necessarily consecutive)</a>, digest of 5 messages in primenumbers Yahoo group, Nov 26 - Nov 27, 2004. [Cached copy]

%o (Python)

%o from sympy import isprime, nextprime

%o m = p_max = 0

%o while m >= 0:

%o     p = 2

%o     while isprime(p + 2*m) == 0:

%o         p = nextprime(p)

%o     if p > p_max:

%o         print(p)

%o         p_max = p

%o     m += 1 # _Ya-Ping Lu_, Sep 24 2020

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

%K nonn

%O 1,1

%A _Jens Kruse Andersen_, Nov 28 2004