A031132 Record differences between n-th prime and (n+2)-nd prime.

3, 4, 6, 10, 12, 14, 18, 24, 28, 40, 42, 44, 48, 50, 56, 58, 72, 76, 80, 82, 100, 114, 116, 126, 138, 140, 160, 190, 200, 234, 236, 246, 248, 270, 306, 328, 330, 336, 340, 372, 376, 410, 436, 438, 450, 476, 502, 506, 524, 540, 546, 594, 600, 624, 678, 690, 700, 760, 780, 838, 900, 944, 972, 1014, 1016, 1032, 1152

Offset

1,1

Links

Table of n, a(n) for n=1..67.

Formula

a(n) = A031134(n) - A031133(n). - Robert G. Wilson v

Example

The difference a(49) = 524 first occurs at prime(2158173265) - prime(2158173263) = 50949283633 - 50949283109 = 524. - Jon E. Schoenfield, Aug 29 2006

Mathematica

d = 0; lst = {}; {p, q, r} = {1, 2, 3}; 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, 212550893}]; Last /@ lst - First /@ lst (* Robert G. Wilson v, May 17 2006 *)
dist = 0; n = 0; While[n<250000000, n++; tmp = Prime[n + 2] - Prime[n]; If[tmp > dist, dist = tmp; Print[tmp]]; ]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 08 2006 *)

Crossrefs

Cf. A031131, A031132, A031133, A031134, A122412, A122413.

See A031133 for lower primes and A031134 for upper primes.

Sequence in context: A082694 A004793 A336909 * A322165 A057477 A309317

Adjacent sequences: A031129 A031130 A031131 * A031133 A031134 A031135

Keyword

nonn

Author

Jeff Burch

Extensions

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

Further extended by Jud McCranie, Jan 03 2001 and again on May 18 2006

a(50)-a(52) from Jon E. Schoenfield, Sep 02 2006

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

a(55) corrected, a(56)-a(62) added by Dmitry Petukhov, Sep 22 2015

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

Status

approved