A316262 Numbers k such that gcd(k, floor(phi*k)) > 1, where phi is the golden ratio.

4, 6, 8, 10, 14, 15, 20, 21, 24, 25, 26, 30, 35, 36, 39, 40, 45, 46, 50, 52, 54, 55, 56, 62, 65, 66, 68, 69, 72, 76, 78, 82, 84, 88, 90, 91, 92, 93, 94, 98, 102, 104, 108, 114, 117, 118, 120, 124, 126, 130, 132, 134, 136, 140, 141, 143, 144, 146, 147, 150

Offset: 1

Author

David V. Feldman, Jun 27 2018

Keywords

• nonn

Examples

			2 divides both 4 and floor(phi*4)=6, so 4 is a term.
		

Crossrefs

Cf. A000201, A001622.

Programs

Maple

select(n->gcd(n,floor(((sqrt(5)-1)/2)*n))>1,[$1..160]); # Muniru A Asiru, Jun 28 2018

Mathematica

Select[Range[150], GCD[#, Floor[GoldenRatio #]] > 1 &] (* Giovanni Resta, Jun 28 2018 *)

PARI

is(n) = gcd(n, floor((sqrt(5)-1)/2*n)) > 1 \\ Felix Fröhlich, Jun 29 2018

Python

from math import gcd, isqrt
from itertools import count, islice
def A316262_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:gcd(n,n+isqrt(5*n**2)>>1)>1,count(max(startvalue,1)))
A316262_list = list(islice(A316262_gen(),30)) # Chai Wah Wu, Aug 10 2022