A031132 - OEIS

%I #43 Oct 06 2019 18:04:51

%S 3,4,6,10,12,14,18,24,28,40,42,44,48,50,56,58,72,76,80,82,100,114,116,

%T 126,138,140,160,190,200,234,236,246,248,270,306,328,330,336,340,372,

%U 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

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

%F a(n) = A031134(n) - A031133(n). - _Robert G. Wilson v_

%e The difference a(49) = 524 first occurs at prime(2158173265) - prime(2158173263) = 50949283633 - 50949283109 = 524. - _Jon E. Schoenfield_, Aug 29 2006

%t 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 *)

%t 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 *)

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

%Y See A031133 for lower primes and A031134 for upper primes.

%K nonn

%O 1,1

%A _Jeff Burch_

%E Extended (and first term added) by _Patrick De Geest_, Oct 15 2000

%E Further extended by _Jud McCranie_, Jan 03 2001 and again on May 18 2006

%E a(50)-a(52) from _Jon E. Schoenfield_, Sep 02 2006

%E a(53)-a(55) from _Dmitry Kamenetsky_, Jul 28 2008

%E a(55) corrected, a(56)-a(62) added by _Dmitry Petukhov_, Sep 22 2015

%E a(63)-a(67) added by _Vladimir Chirkov_ and _Natalia Makarova_, Sep 24 2015, Sep 29 2015