%I #17 Jun 13 2015 00:51:36
%S 1,125,7,49,158,17,58,2,1,1,125,7,49,158,17,58,2,1,1,125,7,49,158,17,
%T 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,
%U 158,17,58,2,1,1,125,7,49,158,17,58,2,1,1,125,7,49,158,17
%N Numerator of the best rational approximation to the decimal representation of the digital roots of m^n, m=1,2,..
%C Sequence has period 9. - _Nathaniel Johnston_, May 05 2011
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1).
%F The digital root of a number m > 0, is d = m mod 9 if d > 0 else d = 9.
%F 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) / ((x-1)*(x^2+x+1)*(x^6+x^3+1)). - _Colin Barker_, Jun 23 2014
%e 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.
%o (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)) }
%o (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) / ((x-1)*(x^2+x+1)*(x^6+x^3+1)) + O(x^100)) \\ _Colin Barker_, Jun 23 2014
%Y Cf. A100406, A100601.
%K base,frac,easy,nonn
%O 1,2
%A _Cino Hilliard_, Jan 02 2005
%E Offset corrected by _Nathaniel Johnston_, May 05 2011