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Search: id:A036118
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| 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The sequence is 12-periodic.
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REFERENCES
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I. M. Vinogradov, Elements of Number Theory, pp. 220 ff.
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FORMULA
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a(n)=1/132*{79*(n mod 12)+46*[(n+1) mod 12]-42*[(n+2) mod 12]+57*[(n+3) mod 12]+35*[(n+4) mod 12]+24*[(n+5) mod 12]-53*[(n+6) mod 12]-20*[(n+7) mod 12]+68*[(n+8) mod 12]-31*[(n+9) mod 12]-9*[(n+10) mod 12]+2*[(n+11) mod 12]) - Paolo P. Lava (ppl(AT)spl.at), Nov 24 2006
a(n)=6.5 + 0*( - 1)^n + ( - 5/3 - 2/3*3^(1/2))*cos(Pi*n/6) + ( - 1/3 - 3^(1/2))*sin(Pi*n/6) - 13/6*cos(Pi*n/2) - 13/6*sin(Pi*n/2) + ( - 5/3 + 2/3*3^(1/2))*cos(5*Pi*n/6) + (3^(1/2) - 1/3)*sin(5*Pi*n/6) [From Richard Choulet (richardchoulet(AT)yahoo.fr), Dec 12 2008]
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MAPLE
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[ seq(primroot(ithprime(i))^j mod ithprime(i), j=0..100) ];
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PROGRAM
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(Other) sage: [power_mod(2, n, 13)for n in xrange(0, 72)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 03 2009]
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CROSSREFS
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Cf. A008831.
Sequence in context: A086317 A110217 A139080 this_sequence A101942 A050170 A087089
Adjacent sequences: A036115 A036116 A036117 this_sequence A036119 A036120 A036121
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KEYWORD
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nonn,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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