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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 October 18 13:31 EDT 2019. Contains 328161 sequences. (Running on oeis4.)