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%I #17 Oct 28 2021 12:37:08
%S 199,1831,5591,30593,81463,82073,162143,173359,404597,542603,544279,
%T 1100977,1444309,2238823,5845193,6752623,6958667,11981443,13626257,
%U 49269581,83751121,147684137,166726367,378043979,895858039,1872851947
%N Increasing peaks in the prime gap sequence A000230.
%C a(n) is the smaller of the two consecutive primes having a late occurring prime gap g = p_k+1 - p_k. All even gaps smaller than g occur at a smaller prime. Also, the next even gap g+2 also occurs earlier.
%D P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 144.
%H Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html">First occurrence prime gaps</a> [For local copy see A000101]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeGaps.html">Prime Gaps</a>
%e 1831 is in this list because the next prime is 1847, giving a prime gap of 16. All even gaps less than 16 occur before this (for smaller primes) and the next even gap, 18, also occurs earlier.
%t lst={};b=max=2;Do[a=2;While[NextPrime@a-a!=2n,a=NextPrime@a];If[a<b&&b>=max,AppendTo[lst,b]];b=a;If[b>max,max=b],{n,40}];lst (* _Giorgos Kalogeropoulos_, Aug 18 2021 *)
%Y Cf. A000230, A001223, A001632, A038664, A086978, A086979, A086980, A002386.
%K nonn
%O 1,1
%A _Harry J. Smith_, Jul 26 2003
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