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A068092 Index of smallest triangular number with n digits. 10
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; text; internal format)
OFFSET

1,2

COMMENTS

Look at the interleaving of the decimal expansion of the square roots of 2 and 20.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..300

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, Mar 08 2004

EXAMPLE

a(4) = 45 as the 45th triangular number is 45*46/2 = 1035 while the 44th is 990.

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} ]

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

CROSSREFS

Cf. A002193, A010476, A068093, A068094, A095863, A095864, A095865, A095866.

Sequence in context: A304068 A005775 A094688 * A255678 A153480 A229007

Adjacent sequences:  A068089 A068090 A068091 * A068093 A068094 A068095

KEYWORD

base,easy,nonn

AUTHOR

Amarnath Murthy, Feb 19 2002

EXTENSIONS

Edited and extended by Robert G. Wilson v, Feb 21 2002

First formula corrected by Ray Chandler, Oct 04 2011

STATUS

approved

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Last modified March 23 05:36 EDT 2019. Contains 321422 sequences. (Running on oeis4.)