A031134 Upper prime of a record difference between it and the second prime before it.

5, 7, 11, 29, 59, 97, 127, 223, 1151, 1361, 2203, 2521, 5639, 9601, 14143, 19661, 19681, 31469, 31477, 38543, 58889, 156007, 360769, 370373, 396871, 1357333, 1562051, 4652507, 8917663, 20831533, 38089453, 70396589, 72546391, 102765847

Offset: 1

Author

Jeff Burch

Keywords

• nonn

Links

• Table of n, a(n) for n = 1..67

Crossrefs

Cf. A031131, A031132, A031133, 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}]; Last /@ lst (* Robert G. Wilson v, May 17 2006 *)

Formula

a(n) = A031133(n) + A031132(n). - Robert G. Wilson v

Extensions

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

Corrected and extended by Jud McCranie, Jan 03 2001

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

Definition corrected by Jon E. Schoenfield, Aug 27 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 25 2015, Sep 29 2015