login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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