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A316262
Numbers k such that gcd(k, floor(phi*k)) > 1, where phi is the golden ratio.
0
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
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
Sequence in context: A310660 A031020 A087270 * A075124 A067315 A069148
KEYWORD
nonn
AUTHOR
David V. Feldman, Jun 27 2018
STATUS
approved