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Integer part of sqrt(n)+sqrt(n+1)+sqrt(n+2)+sqrt(n+3)+sqrt(n+4).
3

%I #19 Sep 08 2022 08:45:23

%S 8,9,11,12,13,14,14,15,16,17,18,18,19,19,20,21,21,22,22,23,23,24,24,

%T 25,25,26,26,27,27,28,28,29,29,29,30,30,31,31,32,32,32,33,33,33,34,34,

%U 34,35,35,36,36,36,37,37,37,38,38,38,39,39,39,39,40,40,40,41,41,41,42,42

%N Integer part of sqrt(n)+sqrt(n+1)+sqrt(n+2)+sqrt(n+3)+sqrt(n+4).

%H Harvey P. Dale, <a href="/A114460/b114460.txt">Table of n, a(n) for n = 1..1000</a>

%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(25n+49)).

%p seq(floor(sqrt(25*n+49)),n=1..90);

%t Table[Floor[Sqrt[25 n + 49]], {n, 80}] (* _Vincenzo Librandi_, Jun 28 2015 *)

%t Floor[Total/@Partition[Sqrt[Range[80]],5,1]] (* _Harvey P. Dale_, Nov 08 2020 *)

%o (PARI) vector(80, n, sqrtint(25*n+49)) \\ _Michel Marcus_, Jun 27 2015

%o (Magma) [Floor(Sqrt(25*n+49)): n in [1..80]]; // _Vincenzo Librandi_, Jun 28 2015

%Y Cf. A000267, A114458, A114459.

%K nonn

%O 1,1

%A _Emeric Deutsch_, Nov 28 2005