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Search: id:A003152
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| A003152 |
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A Beatty sequence: a(n) = floor(n*(1+1/sqrt(2))).
(Formerly M2392)
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+0
6
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| 1, 3, 5, 6, 8, 10, 11, 13, 15, 17, 18, 20, 22, 23, 25, 27, 29, 30, 32, 34, 35, 37, 39, 40, 42, 44, 46, 47, 49, 51, 52, 54, 56, 58, 59, 61, 63, 64, 66, 68, 69, 71, 73, 75, 76, 78, 80, 81, 83, 85, 87, 88, 90, 92, 93, 95, 97, 99, 100, 102, 104, 105, 107, 109, 110, 112, 114, 116
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The g.f. (z+1)*(z**6+2*z**4+z**2+z+1)/(z**6+z**5+z**4+z**3+z**2+z+1)/(z-1)**2 conjectured by S. Plouffe in his 1992 dissertation is wrong.
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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).
L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Pellian representatives, Fib. Quart., 10 (1972), 449-488.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for sequences related to Beatty sequences
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MAPLE
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Digits := 100: t := evalf(1+sin(Pi/4)): A:= n->floor(t*n): seq(floor((t*n)), n=1..68); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 27 2009]
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CROSSREFS
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Complement of A003151.
Cf. A109250.
Sequence in context: A064994 A138235 A059541 this_sequence A068125 A139437 A083042
Adjacent sequences: A003149 A003150 A003151 this_sequence A003153 A003154 A003155
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KEYWORD
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nonn,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 Erich Friedman (erich.friedman(AT)stetson.edu).
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