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 A068092 Index of smallest triangular number with n digits. 10

%I

%S 1,4,14,45,141,447,1414,4472,14142,44721,141421,447214,1414214,

%T 4472136,14142136,44721360,141421356,447213595,1414213562,4472135955,

%U 14142135624,44721359550,141421356237,447213595500,1414213562373

%N Index of smallest triangular number with n digits.

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

%H Vincenzo Librandi, <a href="/A068092/b068092.txt">Table of n, a(n) for n = 1..300</a>

%F a(n) = b where b = floor(sqrt(2*10^(n-1))) and if b(b+1)/2 < 10^(n-1), then b = b+1.

%F a(n) = round((2*10^(n-1))^(1/2)). - _Vladeta Jovovic_, Mar 08 2004

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

%t 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} ]

%o (PARI) a(n) = round(sqrt(2*10^(n-1))) \\ _Charles R Greathouse IV_, Oct 04 2011

%o (MAGMA) [Round(Sqrt(2*10^(n-1))) : n in [1..30]]; // _Vincenzo Librandi_, Oct 05 2011

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

%K base,easy,nonn

%O 1,2

%A _Amarnath Murthy_, Feb 19 2002

%E Edited and extended by _Robert G. Wilson v_, Feb 21 2002

%E First formula corrected by _Ray Chandler_, Oct 04 2011

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Last modified November 14 20:15 EST 2019. Contains 329130 sequences. (Running on oeis4.)