|
|
A286748
|
|
Characteristic sequence of the Beatty sequence, A194028, of sqrt(12).
|
|
3
|
|
|
0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1
|
|
COMMENTS
|
3 + a(n) is almost, but not quite, the length of consecutive runs of same-sign numbers in A088137(m) starting at m=1. To be precise, A088137(m) for m>0 is 1, 2, 1, -4, -11, -10, 13, 56, 73, -22, -263, -460, -131, 1118, 2629, 1904,... which has 3 positive numbers, 3 negative numbers, 3 positive, 4 negative, ... giving the sequence 3,3,3,4, 3,3,4, 3,3,3,4, ..., and aside from that first "3" this is an almost perfect match for 3 + a(n) which begins 4,3,3,4, 3,3,4, 3,3,3,4, ... . Aside from that first term, these two sequences first differ at the 97th term, and differ only 23 times more in the first 400 terms. - Greg Dresden, Oct 06 2019
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 1 - floor((n+1)*(1-1/r)) + floor(n*(1-1/r)), where r = sqrt(12). [corrected by Georg Fischer, Sep 01 2022]
|
|
MATHEMATICA
|
r = Sqrt[12];
s = 1 - Table[Floor[(n + 1) (1 - 1/r) - Floor[n (1 - 1/r)]], {n, 1, 200}] (* A286748 *)
Flatten[Position[s, 0]] (* A286428 *)
Flatten[Position[s, 1]] (* A194028 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|