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 A177148 a(n) = number of squares of summations of digits before reaching the end of the cycle. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified January 21 06:14 EST 2021. Contains 340333 sequences. (Running on oeis4.)