A100601 - OEIS

%I #17 Oct 18 2021 13:34:37

%S 9,1001,50,333,1001,100,333,11,5,9,1001,50,333,1001,100,333,11,5,9,

%T 1001,50,333,1001,100,333,11,5,9,1001,50,333,1001,100,333,11,5,9,1001,

%U 50,333,1001,100,333,11,5,9,1001,50,333,1001,100,333,11,5,9,1001,50

%N Denominator 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*(5*x^8+11*x^7+333*x^6+100*x^5+1001*x^4+333*x^3+50*x^2+1001*x+9) / ((x-1)*(x^2+x+1)*(x^6+x^3+1)). - _Colin Barker_, Jun 23 2014

%F a(n) = a(n-9). - _Wesley Ivan Hurt_, Oct 18 2021

%e 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.

%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*(5*x^8+11*x^7+333*x^6+100*x^5+1001*x^4+333*x^3+50*x^2+1001*x+9) / ((x-1)*(x^2+x+1)*(x^6+x^3+1)) + O(x^100)) \\ _Colin Barker_, Jun 23 2014

%Y Cf. A100406, A100579.

%K base,frac,easy,nonn

%O 1,1

%A _Cino Hilliard_, Jan 02 2005

%E Offset corrected by _Nathaniel Johnston_, May 05 2011