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Search: id:A074840
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| A074840 |
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Numerators a(n) of fractions slowly converging to sqrt(2): let a(1) = 0, b(n) = n - a(n); if (a(n) + 1) / b(n) < sqrt(2), then a(n+1) = a(n) + 1, else a(n+1)= a(n). |
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+0
6
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| 0, 1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 26, 27, 28, 28, 29, 29, 30, 31, 31, 32, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 38, 39, 39, 40, 41, 41, 42, 42, 43, 43
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n) + b(n) = n and as n -> +infinity, a(n) / b(n) converges to sqrt(2). For all n, a(n) / b(n) < sqrt(2).
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FORMULA
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a(1) = 0. b(n) = n - a(n). If (a(n) + 1) / b(n) < sqrt(2), then a(n+1) = a(n) + 1, else a(n+1) = a(n).
a(n) = floor(n*(2-sqrt(2))). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 04 2003
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EXAMPLE
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a(6)= 3 so b(6) = 6 - 3 = 3. a(7) = 4 because (a(6) + 1) / b(6) = 4/3 which is < sqrt(2). So b(7) = 7 - 4 = 3. a(8) = 4 because (a(7) + 1) / b(7) = 5/3 which is not < sqrt(2).
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CROSSREFS
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Cf. A001601.
Sequence in context: A139327 A076905 A098295 this_sequence A064542 A076935 A019446
Adjacent sequences: A074837 A074838 A074839 this_sequence A074841 A074842 A074843
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Robert A. Stump (bee_ess107(AT)msn.com), Sep 09 2002
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