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Search: id:A001951
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| A001951 |
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A Beatty sequence: a(n) = floor[n*sqrt 2].
(Formerly M0955 N0356)
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+0
32
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| 0, 1, 2, 4, 5, 7, 8, 9, 11, 12, 14, 15, 16, 18, 19, 21, 22, 24, 25, 26, 28, 29, 31, 32, 33, 35, 36, 38, 39, 41, 42, 43, 45, 46, 48, 49, 50, 52, 53, 55, 56, 57, 59, 60, 62, 63, 65, 66, 67, 69, 70, 72, 73, 74, 76, 77, 79, 80, 82, 83, 84, 86, 87, 89, 90, 91, 93, 94, 96, 97, 98, 100
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Earliest monotonic sequence >0 satisfying the condition : "a(n)+2n is not in the sequence" - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 25 2004
Also the integer part of the hypotenuse of isosceles right triangles. The real part of these numbers is irrational. For proof see Jones and Jones.
First differences are 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, ..(A006337) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), May 29 2006
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REFERENCES
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L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Pellian representatives, Fib. Quart., 10 (1972), 449-488.
I. G. Connell, A generalization of Wythoff's game, Canad. Math. Bull., 2 (1959), 181-190.
A. S. Fraenkel, How to beat your Wythoff games' opponent on three fronts, Amer. Math. Monthly, 89 (1982), 353-361 (the case a=2).
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 77.
Gareth A. Jones and J. Mary Jones, Elementary Number Theory, Springer, 1998; pp. 221-222.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to Beatty sequences
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PROGRAM
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(PARI) f(n) = for(j=1, n, print1(floor(sqrt(2*j^2))", "))
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CROSSREFS
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Complement of A001952. Equals A001952(n)-2*n.
A003151(n) - n.
Cf. A022342.
Cf. A026250.
A bisection of A094077.
Sequence in context: A014132 A047381 A097506 this_sequence A039046 A026451 A050106
Adjacent sequences: A001948 A001949 A001950 this_sequence A001952 A001953 A001954
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net), Sep 20 2000
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