A335137 a(n) = floor(n*Im(2*e^(i*Pi/5))).

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72

Offset: 1

Author

Karl V. Keller, Jr., May 24 2020

Keywords

• nonn

Comments

This is the Beatty sequence for imaginary part of 2*e^(i*Pi/5).

Im(2*e^(i*Pi/5)) = A182007 = 1.1755705045849462583374119... = 2*sin(Pi/5).

The real part of floor(n*2*e^(i*Pi/5)) is A000201 (floor(n*phi)).

Re(2*e^(i*Pi/5)) = A001622 = phi = (1 + sqrt(5))/2.

For n < 57, a(n) = A109234(n).

Examples

			For n = 3, floor(3*1.17557) = 3.
		

Links

• Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Beatty Sequence.
• Index entries for sequences related to Beatty sequences.

Crossrefs

Cf. A000201, A001622, A109234, A182007.

Programs

Mathematica

Array[Floor[# Im[2 E^(I*Pi/5)]] &, 62] (* Michael De Vlieger, May 24 2020 *)

Python

from sympy import floor, im, exp, I, pi
for n in range(1, 101): print(floor(n*im(2*exp(I*pi/5))), end=', ')