%I #23 Aug 10 2022 22:35:45

%S 4,6,8,10,14,15,20,21,24,25,26,30,35,36,39,40,45,46,50,52,54,55,56,62,

%T 65,66,68,69,72,76,78,82,84,88,90,91,92,93,94,98,102,104,108,114,117,

%U 118,120,124,126,130,132,134,136,140,141,143,144,146,147,150

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

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

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

%t Select[Range[150], GCD[#, Floor[GoldenRatio #]] > 1 &] (* _Giovanni Resta_, Jun 28 2018 *)

%o (PARI) is(n) = gcd(n, floor((sqrt(5)-1)/2*n)) > 1 \\ _Felix Fröhlich_, Jun 29 2018

%o (Python)

%o from math import gcd, isqrt

%o from itertools import count, islice

%o def A316262_gen(startvalue=1): # generator of terms >= startvalue

%o return filter(lambda n:gcd(n,n+isqrt(5*n**2)>>1)>1,count(max(startvalue,1)))

%o A316262_list = list(islice(A316262_gen(),30)) # _Chai Wah Wu_, Aug 10 2022

%Y Cf. A000201, A001622.

%K nonn

%O 1,1

%A _David V. Feldman_, Jun 27 2018