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

1,1

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A045943 A134479 A184969 * A330010 A194114 A127759

Adjacent sequences: A194110 A194111 A194112 * A194114 A194115 A194116

Keyword

nonn

Author

Clark Kimberling, Aug 16 2011

Status

approved