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A182111
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Number of iterations of the map n -> sum of the cubes of the decimal digits of n.
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2
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1, 7, 3, 6, 6, 10, 6, 6, 4, 1, 8, 5, 5, 6, 10, 3, 8, 2, 2, 7, 5, 4, 7, 3, 3, 8, 2, 4, 3, 3, 5, 7, 6, 3, 6, 6, 1, 8, 6, 6, 6, 3, 3, 7, 5, 5, 1, 6, 4, 6, 10, 3, 6, 5, 3, 5, 5, 8, 10, 10, 3, 8, 6, 5, 5, 6, 7, 11, 6, 6, 8, 2, 1, 1, 5, 7, 7, 8, 4, 6, 2, 4, 8, 6, 8
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OFFSET
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1,2
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COMMENTS
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a(n) is the number of times you obtain the sums of cubes of digits of n before reaching a fixed point (last number of the cycle).
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LINKS
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EXAMPLE
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a(3) = 3 because :
3^3 = 27 -> 2^3 + 7^3 = 351;
351 -> 3^3 + 5^3 + 1^3 = 153;
153 -> 1^3+5^3+3^3 = 153 is the end because this number is already in the trajectory. Hence we obtain the map : 3 -> 27 -> 351 -> 153 with 3 iterations.
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MAPLE
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a:= proc(n) local k, m, s; m:= n; s:= {};
for k from 0 do
m:= add(i^3, i=convert(m, base, 10));
if m in s then return k fi;
s:= s union {m}
od
end:
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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