

A100601


Denominator of the best rational approximation to the decimal representation of the digital roots of m^n, m=1,2,..


2



9, 1001, 50, 333, 1001, 100, 333, 11, 5, 9, 1001, 50, 333, 1001, 100, 333, 11, 5, 9, 1001, 50, 333, 1001, 100, 333, 11, 5, 9, 1001, 50, 333, 1001, 100, 333, 11, 5, 9, 1001, 50, 333, 1001, 100, 333, 11, 5, 9, 1001, 50, 333, 1001, 100, 333, 11, 5, 9, 1001, 50
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OFFSET

1,1


COMMENTS

Sequence has period 9.  Nathaniel Johnston, May 05 2011


LINKS

Table of n, a(n) for n=1..57.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).


FORMULA

The digital root of a number m > 0, is d = m mod 9 if d > 0 else d = 9.
G.f.: x*(5*x^8+11*x^7+333*x^6+100*x^5+1001*x^4+333*x^3+50*x^2+1001*x+9) / ((x1)*(x^2+x+1)*(x^6+x^3+1)).  Colin Barker, Jun 23 2014
a(n) = a(n9).  Wesley Ivan Hurt, Oct 18 2021


EXAMPLE

Digital roots of 4^n = 1,4,7,1,4,7,1,4,7,1,4,7,.. 49/333 = 0.147147147147147147147147147147147,.. 333 is the 4th term in the sequence.


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)) }
(PARI) Vec(x*(5*x^8+11*x^7+333*x^6+100*x^5+1001*x^4+333*x^3+50*x^2+1001*x+9) / ((x1)*(x^2+x+1)*(x^6+x^3+1)) + O(x^100)) \\ Colin Barker, Jun 23 2014


CROSSREFS

Cf. A100406, A100579.
Sequence in context: A307324 A327435 A350967 * A260029 A266321 A228293
Adjacent sequences: A100598 A100599 A100600 * A100602 A100603 A100604


KEYWORD

base,frac,easy,nonn


AUTHOR

Cino Hilliard, Jan 02 2005


EXTENSIONS

Offset corrected by Nathaniel Johnston, May 05 2011


STATUS

approved



