OFFSET
1,1
COMMENTS
Sequence has period 9. - Nathaniel Johnston, May 05 2011
LINKS
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) / ((x-1)*(x^2+x+1)*(x^6+x^3+1)). - Colin Barker, Jun 23 2014
a(n) = a(n-9). - 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) / ((x-1)*(x^2+x+1)*(x^6+x^3+1)) + O(x^100)) \\ Colin Barker, Jun 23 2014
CROSSREFS
KEYWORD
base,frac,easy,nonn
AUTHOR
Cino Hilliard, Jan 02 2005
EXTENSIONS
Offset corrected by Nathaniel Johnston, May 05 2011
STATUS
approved