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Search: id:A068092
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| A068092 |
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Index of smallest triangular number with n digits. |
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+0
8
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| 1, 4, 14, 45, 141, 447, 1414, 4472, 14142, 44721, 141421, 447214, 1414214, 4472136, 14142136, 44721360, 141421356, 447213595, 1414213562, 4472135955, 14142135624, 44721359550, 141421356237, 447213595500, 1414213562373
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Look at the interleaving of the decimal expansion of the square roots of 2 and 20.
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FORMULA
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a(n) = b where b = floor[ 2*10^n] and if b(b+1)/2 < 10^n, then b = b+1.
a(n) = round((2*10^(n-1))^(1/2)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 08 2004
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EXAMPLE
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a(4) = 45 as the T45 is 45*46/2 = 1035 while the T44 is 990.
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MATHEMATICA
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f[n_] := Block[{a = Floor[Sqrt[2*10^n]]}, If[a(a + 1)/2 < 10^n, a++ ]; Return[a]]; Table[ f[n], {n, 0, 30} ]
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CROSSREFS
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Cf. A002193, A010476, A068093, A068094, A095863, A095864, A095865, A095866.
Adjacent sequences: A068089 A068090 A068091 this_sequence A068093 A068094 A068095
Sequence in context: A108765 A005775 A094688 this_sequence A117916 A054449 A029868
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KEYWORD
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base,easy,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 19 2002
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 21 2002
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