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

1,1

Links

Table of n, a(n) for n=1..60.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000201, A001622.

Sequence in context: A310660 A031020 A087270 * A075124 A067315 A069148

Adjacent sequences: A316259 A316260 A316261 * A316263 A316264 A316265

Keyword

nonn

Author

David V. Feldman, Jun 27 2018

Status

approved