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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
1
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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
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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.
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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]
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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
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KEYWORD
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nonn,easy
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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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