A100579 Numerator of the best rational approximation to the decimal representation of the digital roots of m^n, m=1,2,..

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

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) / ((x-1)*(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) / ((x-1)*(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