A177148 a(n) = number of squares of summations of digits before reaching the end of the cycle.

0, 0, 5, 2, 4, 4, 2, 3, 3, 1, 1, 5, 2, 4, 4, 2, 3, 3, 1, 2, 5, 2, 4, 4, 2, 3, 3, 1, 2, 5, 2, 4, 4, 2, 3, 3, 1, 2, 5, 2, 4, 4, 2, 3, 3, 1, 2, 5, 2, 2, 4, 2, 3, 3, 1, 2, 5, 2, 2, 3, 2, 3, 3, 1, 2, 5, 2, 2, 3, 2, 3, 3, 1, 2, 5, 2, 2, 3, 2, 2, 3, 1, 2, 5, 2, 2, 3, 2, 2, 4, 1, 2, 5, 2, 2, 3, 2, 2, 4, 2, 1, 5, 2, 4, 4

Offset

0,3

Comments

a(n) is the number of times you form the square of the sum of the digits before reaching the last number of the cycle. According to the computations with Maple program, this last number belong to the set {1,81,100,169,256}, and a(n) < = 5.

Example : 4 -> 16 -> (1+6)^2 = 49 -> (4+9)^2 = 169 -> (1+6+9)^2 = 256, and 256 is the last number of the list because 256 -> (2+5+6)^2 = 169 belong to the list.

Links

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

Example

0 is in the sequence twice because 0->0 and 1 -> 1 ;
5 is in the sequence because : 5 -> 25 -> 49 -> 169 -> 256, last number because 256 -> 169.

Maple

A177148 := proc(n)
        local traj , a, m, c;
        traj := n ;
        c := [n] ;
        while true do
                traj := A118881(traj) ;
                if member(traj, c) then
                        return nops(c)-1 ;
                end if;
                c := [op(c), traj] ;
        end do:
end proc: # R. J. Mathar, Jul 08 2012

Crossrefs

Cf. A118881.

Sequence in context: A021660 A266122 A064853 * A188739 A308171 A265287

Adjacent sequences: A177145 A177146 A177147 * A177149 A177150 A177151

Keyword

nonn,base

Author

Michel Lagneau, May 03 2010

Status

approved