A187396 a(n) = floor(s*n), where s =-2 + sqrt(10); complement of A187395.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 108, 109, 110, 111, 112, 113, 115, 116

Offset: 1

Author

Clark Kimberling, Mar 09 2011

Keywords

• nonn

Comments

A187395 and A187396 are the Beatty sequences based on r = 4 + sqrt(10) and s = -2 + sqrt(10); 1/r + 1/s = 1.

Crossrefs

Cf. A187395.

Programs

Mathematica

r=4+10^(1/2); s=-2+10^(1/2);
Table[Floor[r*n],{n,1,80}]  (* A187395 *)
Table[Floor[s*n],{n,1,80}]  (* A187396 *)

Python

from sympy import integer_nthroot
def A187396(n): return integer_nthroot(10*n**2,2)[0]-2*n # Chai Wah Wu, Mar 17 2021

Formula

a(n) = floor(s*n), where s = -2 + sqrt(10).

Extensions

Edited by Clark Kimberling, Mar 17 2021