A194113 a(n) = Sum_{j=1..n} floor(j*sqrt(10)); n-th partial sum of Beatty sequence for sqrt(10).

3, 9, 18, 30, 45, 63, 85, 110, 138, 169, 203, 240, 281, 325, 372, 422, 475, 531, 591, 654, 720, 789, 861, 936, 1015, 1097, 1182, 1270, 1361, 1455, 1553, 1654, 1758, 1865, 1975, 2088, 2205, 2325, 2448, 2574, 2703, 2835, 2970, 3109, 3251, 3396, 3544

Offset: 1

Author

Clark Kimberling, Aug 16 2011

Keywords

• nonn

Comments

From Marius A. Burtea, Aug 22 2018: (Start)

a(2) = 9 = 3^2;

a(10) = 169 = 13^2;

a(76) = 9216 = 96^2;

a(783) = 970225 = 985^2;

a(5895) = 54952569 = 7413^2;

a(187507) = 55591265284 = 235778^2;

a(577771) = 527815327081 = 726509^2;

...

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Mathematica

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

PARI

for(n=1,50, print1(sum(k=1,n, floor(k*sqrt(10))), ", ")) \\ G. C. Greubel, Sep 24 2017

Python

from math import isqrt
def A194113(n): return sum(isqrt(10*j**2) for j in range(1,n+1)) # Chai Wah Wu, Jul 23 2024