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

1,1

Links

Table of n, a(n) for n=1..46.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A174476 A098645 A089693 * A208951 A299692 A246520

Adjacent sequences: A194113 A194114 A194115 * A194117 A194118 A194119

Keyword

nonn

Author

Clark Kimberling, Aug 16 2011

Status

approved