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Search: id:A083920
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| A083920 |
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Number of nontriangular numbers <= n. |
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+0
2
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| 0, 0, 1, 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, 15, 16, 17, 18, 19, 20, 21, 21, 22, 23, 24, 25, 26, 27, 28, 28, 29, 30, 31, 32, 33, 34, 35, 36, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 55, 56, 57, 58, 59, 60, 61, 62
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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a(t(n))=t(n+1), where t(n)=A000217(n)=n(n+1)/2, the n-th triangular number. For n>=1, a(n)=a(n-1) if and only if n is a triangular number; otherwise, a(n)=1+a(n-1).
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FORMULA
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a(n)=n-Floor((x-1)/2)=n-A003056(n), where x=sqrt(8n+1).
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EXAMPLE
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a(7)=4 counts the nontriangular numbers, 2,4,5,7, that are <=7.
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MATHEMATICA
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f[n_] := n - Floor[(Sqrt[8n + 1] - 1)/2]; Table[ f[n], {n, 0, 73}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Oct 22 2005)
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CROSSREFS
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Cf. A000217, A003056.
Sequence in context: A074184 A093700 A118168 this_sequence A066508 A053207 A138467
Adjacent sequences: A083917 A083918 A083919 this_sequence A083921 A083922 A083923
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), May 08 2003
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