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

Author

Reinhard Zumkeller, May 22 2003

Keywords

• nonn
• easy

Comments

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

Examples

			a(14) = a(2*7) = 1; a(41) = a(5*7+6) = 0.
		

Links

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

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.

Programs

Haskell

a082784 = a000007 . (`mod` 7)
a082784_list = cycle [1,0,0,0,0,0,0]
-- Reinhard Zumkeller, Oct 27 2012

Magma

[Binomial(n-1,6) mod 7 : n in [0..100]]; // Wesley Ivan Hurt, Oct 07 2014

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 *)

PARI

a(n)=!(n%7) \\ Charles R Greathouse IV, Dec 03 2012

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)

Extensions

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