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 A145568 Characteristic function of numbers relatively prime to 11. 10
 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The x-powers appearing in the numerator polynomial of the o.g.f., given below, give the numbers from 0,1,...,10 which survive the sieve of Eratosthenes for multiples of 11, namely 1,2,...10. Contribution from Reinhard Zumkeller, Nov 30 2009: (Start) a(n)=A000007(A010880(n)); a(A160542(n))=1; a(A008593(n))=0; A033443(n) = SUM(a(k)*(n-k): 0<=k<=n). (End) LINKS Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1). FORMULA a(n)=1 if gcd(n,11)=1, else 0. Periodic with period 11: a(n+11)=a(11). O.g.f.: x*sum(x^k,k=0..9)/(1-x^11). a(n)=(n^10 mod 11), with n>=0. a(n)=(1/121)*{13*(n mod 11)+2*[(n+1) mod 11]+2*[(n+2) mod 11]+2*[(n+3) mod 11]+2*[(n+4) mod 11]+2*[(n+5) mod 11]+2*[(n+6) mod 11]+2*[(n+7) mod 11]+2*[(n+8) mod 11]+2*[(n+9) mod 11]-9*[(n+10) mod 11]}, with n>=0. [From Paolo P. Lava, Feb 06 2009] Completely multiplicative with a(p) = (if p=11 then 0 else 1), p prime. [From Reinhard Zumkeller, Nov 30 2009] Dirichlet g.f. (1-11^(-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 LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, 105] (* Ray Chandler, Aug 26 2015 *) PROG (PARI) a(n)=gcd(n, 11)==1 \\ Charles R Greathouse IV, Jun 28 2015 CROSSREFS A000035, A011655, A011558, A109720 for coprimality with 2,3,5,7, respectively. Cf. A168185, A168184, A168182, A168181, A097325, A166486. Sequence in context: A013595 A339145 A011582 * A168185 A011583 A011584 Adjacent sequences:  A145565 A145566 A145567 * A145569 A145570 A145571 KEYWORD nonn,mult,easy AUTHOR Wolfdieter Lang Feb 05 2009 STATUS approved

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Last modified May 9 04:06 EDT 2021. Contains 343685 sequences. (Running on oeis4.)