A194116 a(n) = Sum_{j=1..n} floor(j*sqrt(13)); n-th partial sum of Beatty sequence for sqrt(13).

3, 10, 20, 34, 52, 73, 98, 126, 158, 194, 233, 276, 322, 372, 426, 483, 544, 608, 676, 748, 823, 902, 984, 1070, 1160, 1253, 1350, 1450, 1554, 1662, 1773, 1888, 2006, 2128, 2254, 2383, 2516, 2653, 2793, 2937, 3084, 3235, 3390, 3548, 3710, 3875

Offset: 1

Author

Clark Kimberling, Aug 16 2011

Keywords

• nonn

Crossrefs

Cf. A171983 (Beatty sequence for sqrt(13)).

Programs

Mathematica

c[n_] := Sum[Floor[j*Sqrt[13]], {j, 1, n}];
c = Table[c[n], {n, 1, 90}]

Python

from sympy import integer_nthroot
def A194116(n): return sum(integer_nthroot(13*j**2,2)[0] for j in range(1,n+1)) # Chai Wah Wu, Mar 17 2021