|
|
A188221
|
|
[nr+kr]-[nr]-[kr], where r=sqrt(5), k=1, [ ]=floor.
|
|
3
|
|
|
0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1
|
|
COMMENTS
|
Differs from A188187 in number of initial zeros. This sequence yields right-shift sums (introduced at A187950), and A188187 yields left-shift sums (A188014).
(a(n)) is the Sturmian sequence with slope sqrt(5)-2. This number has continued fraction expansion [0; 4,4,4, ...]. It is therefore fixed point of a morphism sigma, which can be found with the Crisp et al link: sigma is given by 0 -> 0001, 1 -> 00010. - Michel Dekking, Aug 02 2017
|
|
LINKS
|
|
|
FORMULA
|
a(n) = [nr+r]-[nr]-[r], where r=sqrt(5).
|
|
MATHEMATICA
|
r=5^(1/2); k=1;
seqA=Table[Floor[n*r+k*r]-Floor[n*r]-Floor[k*r], {n, 1, 220}] (* A188221 *)
Flatten[Position[seqA, 0] ] (* A188222 *)
Flatten[Position[seqA, 1] ] (* A004976 *)
|
|
PROG
|
(Python)
from sympy import integer_nthroot
def A188221(n): return integer_nthroot(5*(n+1)**2, 2)[0]-integer_nthroot(5*n**2, 2)[0]-2 # Chai Wah Wu, Mar 16 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|