Search: id:A002386
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%I A002386 M0858 N0327
%S A002386 2,3,7,23,89,113,523,887,1129,1327,9551,15683,19609,31397,155921,360653,
%T A002386 370261,492113,1349533,1357201,2010733,4652353,17051707,20831323,
%U A002386 47326693,122164747,189695659,191912783,387096133,436273009,1294268491
%N A002386 Increasing gaps between primes (lower end): primes p(k) where p(k+1)-p(k) 
               exceeds p(j+1)-p(j) for all j<k.
%C A002386 See the links by Jens Kruse Andersen et al. for very large gaps.
%D A002386 B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 
               133.
%D A002386 D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, 
               MA, Vol. 3, Sect 6.1, Table 1.
%D A002386 M. Kraitchik, Recherches sur la Th\'{e}orie des Nombres. Gauthiers-Villars, 
               Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 14.
%D A002386 T. R. Nicely: New maximal prime gaps and first occurrences, Math. Comput. 
               68,227 (1999) 1311-1315.
%D A002386 D. Shanks, On maximal gaps between successive primes, Math. Comp., 18 
               (1964), 646-651.
%D A002386 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002386 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002386 J. Young and A. Potler, First occurrence prime gaps, Math. Comp., 52 
               (1989), 221-224.
%H A002386 M. F. Hasler and N. J. A. Sloane, <a href="b002386.txt">Table of n, a(n) 
               for n=1..74</a> (from the web page of Tomas Oliveira e Silva)
%H A002386 Jens Kruse Andersen, <a href="http://users.cybercity.dk/~dsl522332/math/
               primegaps/gaps20.htm">The Top-20 Prime Gaps</a>
%H A002386 Jens Kruse Andersen, <a href="http://users.cybercity.dk/~dsl522332/math/
               primegaps/megagap2.htm">New record prime gap</a>
%H A002386 Jens Kruse Andersen, <a href="http://users.cybercity.dk/~dsl522332/math/
               primegaps/maximal.htm">Maximal gaps</a>
%H A002386 T. R. Nicely, <a href="http://www.trnicely.net/gaps/gaplist.html">List 
               of prime gaps</a>
%H A002386 Tomas Oliveira e Silva, <a href="http://www.ieeta.pt/~tos/gaps.html">
               Gaps between consecutive primes</a>
%H A002386 Hans Rosenthal and Jens Kruse Andersen, <a href="http://listserv.nodak.edu/
               scripts/wa.exe?A2=ind0401&L=nmbrthry&P=397">A prime megagap</a>
%H A002386 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimeGaps.html">Prime Gaps</a>
%H A002386 <a href="Sindx_Pri.html#gaps">Index entries for primes, gaps between</
               a>
%F A002386 a(n)=A000101(n)-A005250(n)=A008950(n-1)-1 - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), 
               Dec 13 2007
%o A002386 (PARI) a(n)=local(p,g);if(n<2,2*(n>0),p=a(n-1);g=nextprime(p+1)-p;while(p=nextprime(p+1),
               if(nextprime(p+1)-p>g,break));p) - Michael Somos Feb 07 2004
%o A002386 (PARI) p=q=2;g=0;until( g<(q=nextprime(1+p=q))-p & print1(q-g=q-p,","),
               ) \\ - M. F. Hasler, Dec 13 2007
%Y A002386 Cf. A001223, A000101 (upper ends), A005250 (record gaps), A000230.
%Y A002386 Sequence in context: A088173 A129739 A163834 this_sequence A000230 A133429 
               A087770
%Y A002386 Adjacent sequences: A002383 A002384 A002385 this_sequence A002387 A002388 
               A002389
%K A002386 nonn,nice
%O A002386 1,1
%A A002386 N. J. A. Sloane (njas(AT)research.att.com).

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