A082784 Characteristic function of multiples of 7.

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

Offset

0,1

Comments

This sequence is the Euler transformation of A185017. - Jason Kimberley, Oct 14 2011

Links

Table of n, a(n) for n=0..85.

Index entries for characteristic functions.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1).

Formula

a(n) = 0^(n mod 7).

a(0)=1, a(n)=0 for 1<=n<7, a(n+7)=a(n).

a(n) = 1 - (n^6 mod 7). - Paolo P. Lava, Oct 02 2006

a(n) = 1 - A109720(n); a(A008589(n)) = 1; a(A047304(n)) = 0. - Reinhard Zumkeller, Nov 30 2009

a(n) = floor(n/7)-floor((n-1)/7). - Tani Akinari, Oct 26 2012

a(n) = C(n-1,6) mod 7. - Wesley Ivan Hurt, Oct 07 2014

From Wesley Ivan Hurt, Jul 11 2016: (Start)

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

A082784:=n->0^(n mod 7): seq(A082784(n), n=0..100); # Wesley Ivan Hurt, Oct 07 2014

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]
-- Reinhard Zumkeller, Oct 27 2012
(PARI) a(n)=!(n%7) \\ Charles R Greathouse IV, Dec 03 2012
(Magma) [Binomial(n-1, 6) mod 7 : n in [0..100]]; // Wesley Ivan Hurt, Oct 07 2014

Crossrefs

Cf. A008589, A076309.

Characteristic function of multiples of g: A000007 (g=0), A000012 (g=1), A059841 (g=2), A079978 (g=3), A121262 (g=4), A079998 (g=5), A079979 (g=6), this sequence (g=7). - Jason Kimberley, Oct 14 2011

Cf. A000007, A047304, A109720, A185017.

Sequence in context: A015283 A014548 A015087 * A369643 A105165 A058342

Adjacent sequences: A082781 A082782 A082783 * A082785 A082786 A082787

Keyword

nonn,easy

Author

Reinhard Zumkeller, May 22 2003

Extensions

Wrong formula and keyword mult removed by Amiram Eldar, Oct 31 2023

Status

approved