A114458 - OEIS

%I #25 Jul 01 2023 02:44:58

%S 4,5,5,6,7,7,8,8,9,9,10,10,11,11,11,12,12,13,13,13,14,14,14,14,15,15,

%T 15,16,16,16,16,17,17,17,17,18,18,18,18,19,19,19,19,20,20,20,20,20,21,

%U 21,21,21,22,22,22,22,22,23,23,23,23,23,23,24,24,24,24,24,25,25,25,25,25

%N Integer part of sqrt(n)+sqrt(n+1)+sqrt(n+2).

%D Prapanpong Pongsriiam, Analytic Number Theory for Beginners, 2nd edition, American Mathematical Society, 2023.

%H John D. Cook, <a href="https://www.johndcook.com/blog/2023/06/30/floors-and-roots/">Floors and roots</a>.

%H F. D. Hammer, <a href="http://www.jstor.org/stable/2323071">Problem E3010</a>, Amer. Math. Monthly, 95, 1988, 133-134.

%H X. Zhan, <a href="http://dx.doi.org/10.1007/BF02985850">Formulae for sums of consecutive square roots</a>, The Math. Intelligencer, 27, No. 4, 2005, 4-5.

%F a(n) = floor(sqrt(9n+8)).

%p seq(floor(sqrt(9*n+8)),n=1..90);

%t IntegerPart/@(Total/@Partition[Sqrt[Range[80]],3,1]) (* _Harvey P. Dale_, May 03 2013 *)

%o (PARI) vector(80, n, sqrtint(9*n+8)) \\ _Michel Marcus_, Jun 27 2015

%o (Magma) [Floor(Sqrt(9*n+8)): n in [1..70]]; // _Vincenzo Librandi_, Jun 28 2015

%Y Cf. A000267, A114459, A114460.

%K nonn

%O 1,1

%A _Emeric Deutsch_, Nov 28 2005