A194113 - OEIS

%I #38 Jul 23 2024 10:49:16

%S 3,9,18,30,45,63,85,110,138,169,203,240,281,325,372,422,475,531,591,

%T 654,720,789,861,936,1015,1097,1182,1270,1361,1455,1553,1654,1758,

%U 1865,1975,2088,2205,2325,2448,2574,2703,2835,2970,3109,3251,3396,3544

%N a(n) = Sum_{j=1..n} floor(j*sqrt(10)); n-th partial sum of Beatty sequence for sqrt(10).

%C From _Marius A. Burtea_, Aug 22 2018: (Start)

%C   a(2)      =            9 =      3^2;

%C   a(10)     =          169 =     13^2;

%C   a(76)     =         9216 =     96^2;

%C   a(783)    =       970225 =    985^2;

%C   a(5895)   =     54952569 =   7413^2;

%C   a(187507) =  55591265284 = 235778^2;

%C   a(577771) = 527815327081 = 726509^2;

%C   ...

%C Does the sequence include an infinite number of perfect squares? (End)

%H G. C. Greubel, <a href="/A194113/b194113.txt">Table of n, a(n) for n = 1..1000</a>

%t Table[Sum[Floor[j*Sqrt[10]], {j, 1, n}], {n, 1, 90}]

%o (PARI) for(n=1,50, print1(sum(k=1,n, floor(k*sqrt(10))), ", ")) \\ _G. C. Greubel_, Sep 24 2017

%o (Python)

%o from math import isqrt

%o def A194113(n): return sum(isqrt(10*j**2) for j in range(1,n+1)) # _Chai Wah Wu_, Jul 23 2024

%Y Cf. A177102 (Beatty sequence for sqrt(10)).

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 16 2011