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Search: id:A005250
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| A005250 |
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Increasing gaps between primes.
(Formerly M0994)
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+0
28
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| 1, 2, 4, 6, 8, 14, 18, 20, 22, 34, 36, 44, 52, 72, 86, 96, 112, 114, 118, 132, 148, 154, 180, 210, 220, 222, 234, 248, 250, 282, 288, 292, 320, 336, 354, 382, 384, 394, 456, 464, 468, 474, 486, 490, 500, 514, 516, 532, 534, 540, 582, 588, 602, 652
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Here a "gap" means prime(n+1)-prime(n), but in other references it can mean prime(n+1)-prime(n)-1.
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 133.
R. K. Guy, Unsolved Problems in Number Theory, A8.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. Young and A. Potler, First occurrence prime gaps, Math. Comp., 52 (1989), 221-224.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n=1..74 (from the web page of Tomas Oliveira e Silva)
Alex Beveridge, Table giving known values of A000101(n), A005250(n), A107578(n)
C. K. Caldwell, Table of prime gaps
C. K. Caldwell, Gaps up to 1132
T. R. Nicely, Some Results of Computational Research in Prime Numbers
T. R. Nicely, List of Gaps
Tomas Oliveira e Silva, Gaps between consecutive primes
Index entries for primes, gaps between
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FORMULA
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a(n) = A000101(n)-A002386(n) = A008996(n-1) - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Dec 13 2007
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MATHEMATICA
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a=0; s=""; For[i=1, i<10^5, p1=Prime[i]; p2=Prime[i+1]; e=p2-p1; If[e>a, s=s<>ToString[e]<>", "; a=e]; i++ ]; Print[s] (from Vladimir Orlovsky (4vladimir(AT)gmail.com), May 01 2008)
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PROGRAM
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(PARI) p=q=2; g=0; until( g<(q=nextprime(1+p=q))-p & print1(g=q-p, ", "), ) \\ - M. F. Hasler, Dec 13 2007
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CROSSREFS
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Cf. A002386, A000101, A008996, A058320, A107578.
Sequence in context: A152973 A089747 A049015 this_sequence A162762 A156097 A039597
Adjacent sequences: A005247 A005248 A005249 this_sequence A005251 A005252 A005253
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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), R. K. Guy
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EXTENSIONS
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More terms from Andreas Boerner (andreas.boerner(AT)altavista.net), Jul 11 2000. Additional comments from Frank Ellermann (Frank.Ellermann(AT)t-online.de), Apr 20 2001
More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 03 2002; May 01 2006
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