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A068092
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Index of smallest triangular number with n digits.
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Look at the interleaving of the decimal expansion of the square roots of 2 and 20.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..300
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FORMULA
| a(n) = b where b = floor(sqrt(2*10^(n-1))) and if b(b+1)/2 < 10^(n-1), then b = b+1.
a(n) = round((2*10^(n-1))^(1/2)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 08 2004
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EXAMPLE
| a(4) = 45 as the T45 is 45*46/2 = 1035 while the T44 is 990.
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MATHEMATICA
| 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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PROG
| (PARI) a(n) = round(sqrt(2*10^(n-1))) \\ Charles R Greathouse IV, Oct 04 2011
(MAGMA) [Round(Sqrt(2*10^(n-1))) : n in [1..30]]; // Vincenzo Librandi, Oct 05 2011
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CROSSREFS
| Cf. A002193, A010476, A068093, A068094, A095863, A095864, A095865, A095866.
Sequence in context: A108765 A005775 A094688 * A153480 A171851 A117916
Adjacent sequences: A068089 A068090 A068091 * A068093 A068094 A068095
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KEYWORD
| base,easy,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 19 2002
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 21 2002
First formula corrected by Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 04 2011
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