|
|
A082784
|
|
Characteristic function of multiples of 7.
|
|
22
|
|
|
1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 0^(n mod 7).
a(0)=1, a(n)=0 for 1<=n<7, a(n+7)=a(n).
a(n) = floor(n/7)-floor((n-1)/7). - Tani Akinari, Oct 26 2012
G.f.: 1/(1-x^7).
a(n) = a(n-7) for n>6.
a(n) = (gcd(n,7) - 1)/6. (End)
|
|
EXAMPLE
|
a(14) = a(2*7) = 1; a(41) = a(5*7+6) = 0.
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[Mod[Binomial[n - 1, 6], 7], {n, 0, 100}] (* Wesley Ivan Hurt, Oct 07 2014 *)
Table[Boole[Divisible[n, 7]], {n, 0, 100}] (* Amiram Eldar, Oct 31 2023 *)
|
|
PROG
|
(Haskell)
a082784 = a000007 . (`mod` 7)
a082784_list = cycle [1, 0, 0, 0, 0, 0, 0]
(Magma) [Binomial(n-1, 6) mod 7 : n in [0..100]]; // Wesley Ivan Hurt, Oct 07 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Wrong formula and keyword mult removed by Amiram Eldar, Oct 31 2023
|
|
STATUS
|
approved
|
|
|
|