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Search: id:A100406
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| A100406 |
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a(n) = repeating period of the digital roots of the sequence {m^n, m=1,2,3...}. |
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+0
1
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| 1, 124875, 9, 147, 157842, 9, 174, 18, 9, 1, 124875, 9, 147, 157842, 9, 174, 18, 9, 1, 124875, 9, 147, 157842, 9, 174, 18, 9, 1, 124875, 9, 147, 157842, 9, 174, 18, 9, 1, 124875, 9, 147, 157842, 9, 174, 18, 9, 1, 124875, 9, 147, 157842, 9, 174, 18, 9, 1
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sequence has period 9.
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FORMULA
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a(n)=(1/81)*{70843*(n mod 9)+70852*[(n+1) mod 9]+72175*[(n+2) mod 9]+69286*[(n+3) mod 9]+1491268*[(n+4) mod 9]-1348484*[(n+5) mod 9]+69529*[(n+6) mod 9]+1194565*[(n+7) mod 9]-1053095*[(n+8) mod 9]}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Oct 21 2008]
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EXAMPLE
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The digital roots of 1^n are 1,1,1,1,1,1,.. so 1 is the repeating decimal
period for 1^n. The digital roots of 2^n are 1,2,4,8,7,5.. so 125875 is the
repeating decimal period for 2^n. The digital roots of 3^n are 1,3,9,9,9,9,..
so 9 is the repeating decimal period for 3^n.
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PROGRAM
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(PARI) f(n, m) = for(x=0, n, print1(droot(m^x)", ")) droot(n) = \ the digital root of a number. { local(x); x= n%9; if(x>0, return(x), return(9)) }
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CROSSREFS
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Sequence in context: A049358 A061734 A030639 this_sequence A048936 A133220 A023086
Adjacent sequences: A100403 A100404 A100405 this_sequence A100407 A100408 A100409
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KEYWORD
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easy,nonn,base
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Dec 31 2004
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