A081503 Number of steps to reach a single digit when map in A081502 is iterated.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3

Offset: 0

Author

N. J. A. Sloane, Apr 22 2003

Keywords

• nonn
• easy
• base

Examples

			19 -> 3+9 = 12 -> 3+2 = 5, taking 2 steps, so a(19)=2.
		

Programs

Maple

A081503 := proc(n)
    local nitr,a ;
    nitr := n ;
    a := 0 ;
    while nitr > 9 do
        nitr := A081502(nitr) ;
        a := a+1 ;
    end do;
    a ;
end proc: # R. J. Mathar, Oct 03 2014

Formula

a(n) = O(log n).

Extensions

More terms from Matthew Conroy, Jan 16 2006

Formula from Charles R Greathouse IV, Aug 02 2010