This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A182128 #16 Jan 30 2022 02:44:25 %S A182128 0,0,2,3,3,2,3,3,1,2,1,2,3,3,2,3,3,1,2,2,2,3,3,2,3,3,1,2,2,2,3,3,2,3, %T A182128 3,1,2,2,2,2,3,2,3,3,1,2,2,2,2,3,2,3,3,1,2,2,2,2,3,2,3,3,1,2,2,2,2,3, %U A182128 2,2,3,1,2,2,2,2,3,2,2,3,1,2,2,2,2,3,2 %N A182128 Number of iterations of the map n -> (sum of the decimal digits of n)^3 before reaching the last number of the cycle. %C A182128 a(n) is the number of times that the cube of the sum of the digits must be calculated before reaching the last number of the cycle. %e A182128 0 is in the sequence twice because 0 -> 0 and 1 -> 1; %e A182128 a(3) = 3: %e A182128 3 -> 3^3 = 27; %e A182128 27 -> (2+7)^3 = 729; %e A182128 729 -> (7+2+9)^3 = 18^3 = 5832 is the end of the map because 5832 -> (5+8+3+2)^3 = 18^3 is already in the trajectory. Hence we obtain the map: 3 -> 27 -> 729 -> 5832 with 3 iterations. %p A182128 A182128 := proc(n) %p A182128 local traj ,c; %p A182128 traj := n ; %p A182128 c := [n] ; %p A182128 while true do %p A182128 traj := A118880(traj) ; %p A182128 if member(traj,c) then %p A182128 return nops(c)-1 ; %p A182128 end if; %p A182128 c := [op(c),traj] ; %p A182128 end do: %p A182128 end proc: %p A182128 seq(A182128(n),n=0..80) ; # _R. J. Mathar_, Jul 08 2012 %Y A182128 Cf. A177148, A178481, A118880. %K A182128 nonn,base %O A182128 0,3 %A A182128 _Michel Lagneau_, Apr 13 2012