

A100406


a(n) = repeating period of the digital roots of the sequence {m^n, m=1,2,3...}.


2



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
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OFFSET

1,2


COMMENTS

Sequence has period 9.


LINKS

Table of n, a(n) for n=1..55.


FORMULA

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, Oct 21 2008]


EXAMPLE

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.


PROG

(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)) }


CROSSREFS

Cf. A100579, A100601.
Sequence in context: A061734 A030639 A182658 * A183797 A234783 A206134
Adjacent sequences: A100403 A100404 A100405 * A100407 A100408 A100409


KEYWORD

easy,nonn,base


AUTHOR

Cino Hilliard, Dec 31 2004


EXTENSIONS

Offset corrected by Nathaniel Johnston, May 05 2011


STATUS

approved



