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A081742
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a(1)=1; then if n is a multiple of 3, a(n) = a(n/3) + 1; if n is not a multiple of 3 but even, a(n) = a(n/2) + 1; a(n) = a(n-1) + 1 otherwise.
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2
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1, 2, 2, 3, 4, 3, 4, 4, 3, 5, 6, 4, 5, 5, 5, 5, 6, 4, 5, 6, 5, 7, 8, 5, 6, 6, 4, 6, 7, 6, 7, 6, 7, 7, 8, 5, 6, 6, 6, 7, 8, 6, 7, 8, 6, 9, 10, 6, 7, 7, 7, 7, 8, 5, 6, 7, 6, 8, 9, 7, 8, 8, 6, 7, 8, 8, 9, 8, 9, 9, 10, 6, 7, 7, 7, 7, 8, 7, 8, 8, 5, 9, 10, 7, 8, 8, 8, 9, 10, 7, 8, 10, 8, 11, 12, 7, 8, 8, 8, 8, 9, 8
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OFFSET
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1,2
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COMMENTS
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A stopping problem: number of steps to reach zero starting with n and applying: x -> x/3 if x is a multiple of 3, x -> x/2 if x is even and not a multiple of 3, x -> x-1 otherwise.
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LINKS
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FORMULA
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a(n)/log(n) is bounded.
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MAPLE
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f:= proc(n) option remember;
if n mod 3 = 0 then procname(n/3)+1
elif n::even then procname(n/2)+1
else procname(n-1)+1
fi
end proc:
f(1):= 1:
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MATHEMATICA
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a[n_] := a[n] = Which[n == 1, 1, Divisible[n, 3], a[n/3]+1, EvenQ[n], a[n/2]+1, True, a[n-1]+1];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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