

A100579


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


2



1, 125, 7, 49, 158, 17, 58, 2, 1, 1, 125, 7, 49, 158, 17, 58, 2, 1, 1, 125, 7, 49, 158, 17, 58, 2, 1, 1, 125, 7, 49, 158, 17, 58, 2, 1, 1, 125, 7, 49, 158, 17, 58, 2, 1, 1, 125, 7, 49, 158, 17, 58, 2, 1, 1, 125, 7, 49, 158, 17, 58, 2, 1, 1, 125, 7, 49, 158, 17
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OFFSET

1,2


COMMENTS

Sequence has period 9.  Nathaniel Johnston, May 05 2011


LINKS

Table of n, a(n) for n=1..69.
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*(x^8+2*x^7+58*x^6+17*x^5+158*x^4+49*x^3+7*x^2+125*x+1) / ((x1)*(x^2+x+1)*(x^6+x^3+1)).  Colin Barker, Jun 23 2014


EXAMPLE

Digital roots of 4^n = 1,4,7,1,4,7,1,4,7,1,4,7,... 49/333 = 0.147147147147147147147147147147147,.. 49 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*(x^8+2*x^7+58*x^6+17*x^5+158*x^4+49*x^3+7*x^2+125*x+1) / ((x1)*(x^2+x+1)*(x^6+x^3+1)) + O(x^100)) \\ Colin Barker, Jun 23 2014


CROSSREFS

Cf. A100406, A100601.
Sequence in context: A227393 A005080 A174733 * A298062 A298711 A088403
Adjacent sequences: A100576 A100577 A100578 * A100580 A100581 A100582


KEYWORD

base,frac,easy,nonn


AUTHOR

Cino Hilliard, Jan 02 2005


EXTENSIONS

Offset corrected by Nathaniel Johnston, May 05 2011


STATUS

approved



