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 A109720 Periodic sequence {0,1,1,1,1,1,1} or n^6 mod 7. 17
 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 (list; graph; refs; listen; history; text; internal format)
 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 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) = (1/49)*{9*(n mod 7)+2*[(n+1) mod 7]+2*[(n+2) mod 7]+2*[(n+3) mod 7]+2*[(n+4) mod 7]+2*[(n+5) mod 7]-5*[(n+6) mod 7]}. - Paolo P. Lava, Nov 21 2006 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

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Last modified May 9 05:11 EDT 2021. Contains 343688 sequences. (Running on oeis4.)