A109720 Periodic sequence {0,1,1,1,1,1,1} or n^6 mod 7.

0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1

Offset

0,1

Comments

This sequence also represents n^12 mod 7; n^18 mod 7; (exponents are = 0 mod 6).

Characteristic sequence for numbers n>=1 to be relatively prime to 7. - Wolfdieter Lang, Oct 29 2008

a(n+4), n>=0, (periodic 1,1,1,0,1,1,1) is also the characteristic sequence for mod m reduced positive odd numbers (i.e., gcd(2*n+1,m)=1, n>=0) for each modulus m from 7*A003591 = [7,14,28,49,56,98,112,196,...]. [Wolfdieter Lang, Feb 04 2012]

Links

Table of n, a(n) for n=0..104.

Index entries for characteristic functions - Reinhard Zumkeller, Nov 30 2009

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

Formula

a(n) = 0 if n=0 mod 7; a(n)= 1 else.

G.f. = (x+x^2+x^3+x^4+x^5+x^6)/(1-x^7)= -x*(1+x)*(1+x+x^2)*(x^2-x+1) / ( (x-1)*(1+x+x^2+x^3+x^4+x^5+x^6) ).

a(n)=1-A082784(n); a(A047304(n))=1; a(A008589(n))=0; A033439(n) = SUM(a(k)*(n-k): 0<=k<=n). - Reinhard Zumkeller, Nov 30 2009

Multiplicative with a(p) = (if p=7 then 0 else 1), p prime. - Reinhard Zumkeller, Nov 30 2009

Dirichlet g.f. (1-7^(-s))*zeta(s). - R. J. Mathar, Mar 06 2011

For the general case: the characteristic function of numbers that are not multiples of m is a(n)=floor((n-1)/m)-floor(n/m)+1, m,n > 0. - Boris Putievskiy, May 08 2013

Mathematica

PadRight[{}, 120, {0, 1, 1, 1, 1, 1, 1}] (* Harvey P. Dale, Jul 09 2018 *)

Prog

(Sage) [power_mod(n, 6, 7)for n in range(0, 105)] # Zerinvary Lajos, Nov 06 2009
(PARI) a(n)=n^6%7 \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

Cf. A010876 = n mod 7; A053879 = n^2 mod 7; A070472 = m^3 mod 7; A070512 = n^4 mod 7; A070593 = n^5 mod 7.

Cf. A168185, A145568, A168184, A168182, A168181, A097325, A011558, A166486, A011655, A000035.

Sequence in context: A341591 A306453 A175629 * A022932 A334812 A079421

Adjacent sequences: A109717 A109718 A109719 * A109721 A109722 A109723

Keyword

easy,mult,nonn

Author

Bruce Corrigan (scentman(AT)myfamily.com), Aug 09 2005

Status

approved