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A005250
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Increasing gaps between primes.
(Formerly M0994)
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34
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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;
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listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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. P. Brent, J. H. Osborn and W. D. Smith, Lower bounds on maximal determinants of +-1 matrices via the probabilistic method, arXiv preprint arXiv:1211.3248, 2012. - From N. J. A. Sloane, Jan 02 2013
R. K. Guy, Unsolved Problems in Number Theory, A8.
A. Kourbatov, Maximal gaps between prime k-tuples: a statistical approach, arXiv preprint arXiv:1301.2242, 2013. - From N. J. A. Sloane, Feb 09 2013
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Marek Wolf, A Note on the Andrica Conjecture, arXiv:1010.3945.
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..75
Jens Kruse Andersen, The Top-20 Prime Gaps
Jens Kruse Andersen, New record prime gap
Jens Kruse Andersen, Maximal gaps
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, 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 Joseph Stephan Orlovsky, May 01 2008)
nn=10^7; Module[{d=Differences[Prime[Range[nn]]], ls={1}}, Table[If[d[[n]]> Last[ls], AppendTo[ls, d[[n]]]], {n, nn-1}]; ls] (* Harvey P. Dale, Jul 23 2012 *)
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PROG
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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
(Haskell)
a005250 n = a005250_list !! (n-1)
a005250_list = f 0 a001223_list
where f m (x:xs) = if x <= m then f m xs else x : f x xs
-- Reinhard Zumkeller, Dec 12 2012
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CROSSREFS
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Cf. A002386, A000101, A008996, A058320, A107578.
Sequence in context: A089747 A173144 A049015 * A162762 A156097 A039597
Adjacent sequences: A005247 A005248 A005249 * 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, 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, Apr 20 2001
More terms from Robert G. Wilson v, Jan 03 2002; May 01 2006
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STATUS
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approved
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