A194151 -id:A194151

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Search: a194151 -id:a194151

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page 1

A194152

Beatty sequence for 5+2*sqrt(5); complement of A194151.

+20
2

9, 18, 28, 37, 47, 56, 66, 75, 85, 94, 104, 113, 123, 132, 142, 151, 161, 170, 179, 189, 198, 208, 217, 227, 236, 246, 255, 265, 274, 284, 293, 303, 312, 322, 331, 340, 350, 359, 369, 378, 388, 397, 407, 416, 426, 435, 445, 454, 464, 473, 483, 492, 502

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 5*n + A022839(2*n). - R. J. Mathar, Aug 25 2011

a(n) = floor(n*(5+2*sqrt(5))). - Vincenzo Librandi, Oct 25 2011

MATHEMATICA

r=Sqrt[5]/2;

c[k_]:=Floor[k*r];

Table[c[k], {k, 1, 90}] (* A194151 *)

s=5+2*Sqrt[5];

d[k_]:=Floor[k*s];

Table[d[k], {k, 1, 90}] (* A194152 *)

PROG

(Magma) [Floor(n*(5+2*Sqrt(5))): n in [1..80]]; // Vincenzo Librandi, Oct 25 2011

(Python)

from sympy import integer_nthroot

def A194152(n): return 5*n+integer_nthroot(20*n**2, 2)[0] # Chai Wah Wu, Mar 16 2021

CROSSREFS

Cf. A022839, A194151.

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 17 2011

STATUS

approved

A194153

Sum{floor(j*(sqrt(5))/2) : 1<=j<=n}; n-th partial sum of Beatty sequence for (sqrt(5))/2.

+10
0

1, 3, 6, 10, 15, 21, 28, 36, 46, 57, 69, 82, 96, 111, 127, 144, 163, 183, 204, 226, 249, 273, 298, 324, 351, 380, 410, 441, 473, 506, 540, 575, 611, 649, 688, 728, 769, 811, 854, 898, 943, 989, 1037, 1086, 1136, 1187, 1239, 1292, 1346, 1401, 1458, 1516