|
|
A074778
|
|
Numbers k such that 2^k+1 and F(k) are not relatively prime, where F(k) denotes the k-th Fibonacci number.
|
|
1
|
|
|
10, 14, 30, 36, 42, 50, 54, 70, 74, 90, 98, 100, 108, 110, 114, 126, 130, 134, 150, 154, 162, 170, 174, 178, 180, 182, 190, 192, 194, 202, 210, 222, 230, 238, 250, 252, 254, 266, 270, 290, 294, 300, 310, 322, 324, 330, 340, 342, 350, 352, 354, 370, 378, 390
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
If n is in the sequence, then so is k*n for all odd k. - Robert Israel, Jan 10 2018
|
|
LINKS
|
|
|
FORMULA
|
a(n) seems to be asymptotic to c*n with c=5.8...
|
|
MAPLE
|
N:= 100:
R:= NULL:
count:= 0:
for n from 1 while count < N do
if igcd(2^n+1, combinat:-fibonacci(n)) > 1 then
count:= count+1;
R:= R, n
fi
od:
|
|
MATHEMATICA
|
Select[Range[400], !CoprimeQ[2^# + 1, Fibonacci[#]] &] (* Amiram Eldar, May 20 2022 *)
|
|
PROG
|
(PARI) isok(n) = gcd(2^n+1, fibonacci(n)) != 1; \\ Michel Marcus, Jan 10 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|