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A068092
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Index of smallest triangular number with n digits.
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12
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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, 4472135955000, 14142135623731
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OFFSET
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1,2
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COMMENTS
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Look at the interleaving of the decimal expansion of the square roots of 2 and 20.
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LINKS
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FORMULA
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a(n) = b where b = floor(sqrt(2*10^(n-1))) and if b(b+1)/2 < 10^(n-1), then b = b+1. [corrected by _Ray Chandler_, Oct 04 2011]
a(n) = round((2*10^(n-1))^(1/2)). - _Vladeta Jovovic_, Mar 08 2004
a(n) = A002024(10^(n-1)). - _Michel Marcus_, Jan 27 2022
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EXAMPLE
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a(4) = 45 as the 45th triangular number is 45*46/2 = 1035 while the 44th 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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PROG
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(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
(Python)
from math import isqrt
def A068092(n): return isqrt(10**(n-1)<<3)+1>>1 # _Chai Wah Wu_, Oct 17 2022
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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_Amarnath Murthy_, Feb 19 2002
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EXTENSIONS
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Edited and extended by _Robert G. Wilson v_, Feb 21 2002
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STATUS
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approved
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