A031133 Lower prime of a record difference between it and the second prime after it.

2, 3, 5, 19, 47, 83, 109, 199, 1123, 1321, 2161, 2477, 5591, 9551, 14087, 19603, 19609, 31393, 31397, 38461, 58789, 155893, 360653, 370247, 396733, 1357193, 1561891, 4652317, 8917463, 20831299, 38089217, 70396343, 72546143, 102765577

Offset: 1

Author

Jeff Burch

Keywords

• nonn

Links

• Table of n, a(n) for n = 1..67

Crossrefs

Cf. A031131, A031132, A031134, A122412, A122413.

Programs

Mathematica

lst = {}; {p, q, r} = {1, 2, 3}; d = 0; Do[{p, q, r} = {q, r, Prime@n}; If[r - p > d, d = r - p; AppendTo[lst, {p, r}]; Print[{p, r-p, r}]], {n, 8050000}]; First /@ lst (* Robert G. Wilson v, May 17 2006 *)

PARI

gap=0;p=2;q=3;forprime(r=5,1e9,if(r-p>gap,gap=r-p;print1(p", ")); p=q;q=r) \\ Charles R Greathouse IV, Mar 06 2013

Formula

a(n) = A031134(n) - A031132(n). - Robert G. Wilson v

Extensions

Extended (and first term added) by Patrick De Geest, Oct 15 2000

Further extended by Jud McCranie, Jan 03 2001

a(34)-a(52) from Jon E. Schoenfield, Sep 02 2006

a(53)-a(55) added by Dmitry Kamenetsky, Jul 28 2008

a(55) corrected, a(56)-a(62) added by Dmitry Petukhov, Sep 20 2015

a(63)-a(67) added by Vladimir Chirkov and Natalia Makarova, Sep 24 2015, Sep 29 2015