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

0,18

Links

Table of n, a(n) for n=0..104.

Formula

a(n) = O(log n).

Example

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

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

Crossrefs

Sequence in context: A037804 A316894 A362933 * A351206 A176508 A241492

Adjacent sequences: A081500 A081501 A081502 * A081504 A081505 A081506

Keyword

nonn,easy,base

Author

N. J. A. Sloane, Apr 22 2003

Extensions

More terms from Matthew Conroy, Jan 16 2006

Formula from Charles R Greathouse IV, Aug 02 2010

Status

approved