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A177148
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a(n) = number of squares of summations of digits before reaching the end of the cycle.
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5
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..104.
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EXAMPLE
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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.
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MAPLE
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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
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CROSSREFS
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Cf. A118881.
Sequence in context: A021660 A266122 A064853 * A188739 A308171 A265287
Adjacent sequences: A177145 A177146 A177147 * A177149 A177150 A177151
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KEYWORD
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nonn,base
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AUTHOR
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Michel Lagneau, May 03 2010
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STATUS
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approved
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