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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
OFFSET
1
COMMENTS
The positions of 0 are given by A286428, and of 1, by A194028.
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
Sequence in context: A182581 A288203 A238470 * A289001 A171588 A289035
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 15 2017
STATUS
approved