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Search: id:A002386
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| A002386 |
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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.
(Formerly M0858 N0327)
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+0
26
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| 2, 3, 7, 23, 89, 113, 523, 887, 1129, 1327, 9551, 15683, 19609, 31397, 155921, 360653, 370261, 492113, 1349533, 1357201, 2010733, 4652353, 17051707, 20831323, 47326693, 122164747, 189695659, 191912783, 387096133, 436273009, 1294268491
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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See the links by Jens Kruse Andersen et al. for very large gaps.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 133.
D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 3, Sect 6.1, Table 1.
M. Kraitchik, Recherches sur la Th\'{e}orie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 14.
T. R. Nicely: New maximal prime gaps and first occurrences, Math. Comput. 68,227 (1999) 1311-1315.
D. Shanks, On maximal gaps between successive primes, Math. Comp., 18 (1964), 646-651.
J. Young and A. Potler, First occurrence prime gaps, Math. Comp., 52 (1989), 221-224.
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LINKS
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M. F. Hasler and N. J. A. Sloane, Table of n, a(n) for n=1..74 (from the web page of Tomas Oliveira e Silva)
Jens Kruse Andersen, The Top-20 Prime Gaps
Jens Kruse Andersen, New record prime gap
Jens Kruse Andersen, Maximal gaps
T. R. Nicely, List of prime gaps
Tomas Oliveira e Silva, Gaps between consecutive primes
Hans Rosenthal and Jens Kruse Andersen, A prime megagap
Eric Weisstein's World of Mathematics, Prime Gaps
Index entries for primes, gaps between
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FORMULA
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a(n)=A000101(n)-A005250(n)=A008950(n-1)-1 - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Dec 13 2007
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PROGRAM
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(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
(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
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CROSSREFS
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Cf. A001223, A000101 (upper ends), A005250 (record gaps), A000230.
Adjacent sequences: A002383 A002384 A002385 this_sequence A002387 A002388 A002389
Sequence in context: A088173 A129739 A163834 this_sequence A000230 A133429 A087770
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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