A089808 a(n) = floor(1/((n*r) mod 1)), where r = phi^(-2) = (3 - sqrt(5))/2.

2, 1, 6, 1, 1, 3, 1, 17, 2, 1, 4, 1, 1, 2, 1, 8, 2, 1, 3, 1, 46, 2, 1, 5, 1, 1, 3, 1, 12, 2, 1, 4, 1, 1, 2, 1, 7, 1, 1, 3, 1, 23, 2, 1, 5, 1, 1, 2, 1, 10, 2, 1, 4, 1, 122, 2, 1, 6, 1, 1, 3, 1, 15, 2, 1, 4, 1, 1, 2, 1, 8, 1, 1, 3, 1, 33, 2, 1, 5, 1, 1, 3, 1, 11, 2, 1, 4, 1, 1, 2, 1, 7, 1, 1, 3, 1, 19, 2, 1, 5, 1

Offset: 1

Author

Gary W. Adamson, Nov 11 2003

Keywords

• nonn
• easy

Comments

1. a(n) = 1 iff A024569 is not 1, (A024569 = 1, 4, 1, 2, 11, 1, 3, 1, 1, ...)

2. a(n) = 1 iff A078588 = 0.

3. a(n) = 1 iff A089809 = 1.

Examples

			a(6) = 3. Take 6*r = 2.29179...( mod 1) = 0.29179...; invert = 3.42705... and delete the fractional part, getting 3.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A024569, A078588, A089809.

Programs

Mathematica

r := (3 - Sqrt[5])/2; Table[Floor[1/(Mod[(n*r), 1])], {n, 1, 50}] (* G. C. Greubel, Nov 20 2017 *)

Extensions

More terms from Sam Alexander, Nov 16 2003