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Search: id:A145568
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| A145568 |
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Characteristic sequence for numbers to be relatively prime to 11. |
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+0
11
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| 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; listen)
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OFFSET
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0,1
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COMMENT
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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 (reinhard.zumkeller(AT)gmail.com), 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)
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LINKS
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Index entries for characteristic functions [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
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FORMULA
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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 (ppl(AT)spl.at), Feb 06 2009]
Multiplicative with a(p) = (if p=11 then 0 else 1), p prime. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
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CROSSREFS
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A000035, A011655, A011558, A109720 for coprimality with 2,3,5,7, respectively.
Sequence in context: A164980 A013595 A011582 this_sequence A123927 A011583 A011584
Adjacent sequences: A145565 A145566 A145567 this_sequence A145569 A145570 A145571
Cf. A168185, A168184, A168182, A168181, A097325, A166486. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
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KEYWORD
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nonn,easy,new
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Feb 05 2009
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