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%I #57 May 17 2024 02:32:49
%S 1,2,4,14,22,34,52,72,86,96,112,132,148,180,210,248,282,320,336,354,
%T 382,456,514,532,582,588,602,652,716,766,906,1132,1328,1356,1370,1442,
%U 1476,1572
%N Prime gaps q-p with n-th record merit referred to in A111870.
%C The prime gaps q-p (corresponding to a(n)=p in A111870) have increasing record merit (q-p)/log(p). However, the prime gaps themselves are almost always monotonically increasing (with very high probability), but not always! And we do have an exception in the list above: a(14)=148 < a(13)=154! (But see next comment!)
%C Because the erroneous A111870(13) = 4652353 term was removed, a(13) = 154 was removed. This sequence is therefore monotonically increasing. - _John W. Nicholson_, Nov 18 2013
%D Ed Pegg, Jr., Posting to Seq Fan mailing list, Nov 23, 2005
%H Jens Kruse Andersen, Norman Luhn, <a href="https://www.pzktupel.de/JensKruseAndersen/risinggap.php">Record prime gaps</a>.
%F a(n) = A277552(n) - A111870(n). - _Bobby Jacobs_, Nov 13 2016
%e A111870(4) = 113 and the next larger prime is 127, so 127 - A111870(4) = a(4) = 14.
%Y For the primes p corresponding to the prime gaps q-p with n-th record merit, see A111870.
%Y Cf. A002386, A277552.
%K nonn,hard,more
%O 1,2
%A _N. J. A. Sloane_, based on correspondence with _Ed Pegg Jr_, Nov 23 2005
%E Corrected and edited by _Daniel Forgues_, Nov 11 2009 and Nov 20 2009
%E Because the erroneous A111870(13) = 4652353 term was removed, a(13) = 154 was removed by _John W. Nicholson_, Nov 18 2013
%E a(33)-a(35) inserted by _Bobby Jacobs_, Nov 08 2016
%E a(37) added by _Bobby Jacobs_, Nov 09 2016
%E a(38) added by _Rodolfo Ruiz-Huidobro_, May 14 2024
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