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 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 a(0)=1, a(n)=0 for 1<=n<7, a(n+7)=a(n). a(n) = 1-A109720(n); a(A008589(n))=1; a(A047304(n))=0. - Reinhard Zumkeller, Nov 30 2009 This sequence is the Euler transformation of A185017. - Jason Kimberley, Oct 14 2011 LINKS Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1). FORMULA a(n) = 0^(n mod 7). a(n) = (1/147)*(-20*(n mod 7)+((n+1) mod 7)+((n+2) mod 7)+((n+3) mod 7)+((n+4) mod 7)+((n+5) mod 7)+22*((n+6) mod 7)). - Paolo P. Lava, Sep 29 2006 a(n) = 1-(n^6 mod 7). - Paolo P. Lava, Oct 02 2006 Multiplicative with a(p) = (if p=7 then 1 else 0), p prime. - 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 *) 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. Sequence in context: A015283 A014548 A015087 * A105165 A058342 A205808 Adjacent sequences:  A082781 A082782 A082783 * A082785 A082786 A082787 KEYWORD nonn,easy AUTHOR Reinhard Zumkeller, May 22 2003 STATUS approved

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Last modified September 29 14:13 EDT 2020. Contains 337431 sequences. (Running on oeis4.)