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A212813
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Number of steps for n to reach 8 under iteration of the map i -> A036288(i), or -1 if 8 is never reached.
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8
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-1, -1, -1, -1, -1, -1, 1, 0, 2, 1, 2, 1, 3, 2, 3, 3, 4, 3, 3, 2, 3, 3, 3, 2, 3, 4, 2, 2, 4, 3, 4, 3, 4, 3, 4, 3, 5, 4, 5, 2, 5, 4, 5, 4, 2, 5, 3, 2, 4, 4, 4, 4, 3, 2, 5, 3, 4, 4, 5, 4, 5, 4, 3, 4, 4, 5, 5, 4, 3, 4, 5, 4, 4, 3, 3, 3, 4, 4, 4, 3, 4, 5, 5, 4, 4, 6, 5, 4, 4, 3, 4, 3, 5, 5, 4, 3, 6, 5, 4, 4, 5, 4, 4, 3, 4, 4, 4, 3, 5, 4, 6, 4, 5, 4, 5, 4, 3, 5, 4
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OFFSET
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1,9
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COMMENTS
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It is known that a(n) >= 0 for n >= 7. Bellamy and Cadogan call a(n) the "class number" of n, but this is not a good idea as this term is already overworked.
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REFERENCES
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Bellamy, O. S.; Cadogan, C. C. Subsets of positive integers: their cardinality and maximality properties. Proceedings of the Tenth Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1979), pp. 167--178, Congress. Numer., XXIII-XXIV, Utilitas Math., Winnipeg, Man., 1979. MR0561043 (82b:10006)
R. Honsberger, Mathematical Morsels, MAA, 1978, p. 223.
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LINKS
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MAPLE
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f:=proc(n) local i, t1; t1:=ifactors(n)[2]; 1+add( t1[i][1]*t1[i][2], i=1..nops(t1)); end; # this is A036288
g:=proc(n) local i, t1; global f; t1:=n; for i from 1 to 1000 do if t1=8 then RETURN(i-1); fi; t1:=f(t1); od; -1; end; # this is A212813
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MATHEMATICA
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imax = 11 (* = max term plus 1 *);
a36288[n_] := If[n == 1, 1, Total[Times @@@ FactorInteger[n]] + 1];
a[n_] := Module[{i, k}, For[k = n; i = 1, i <= imax, i++, If[k == 8, Return[i - 1]]; k = a36288[k]]; If[n > 6, Print["imax ", imax, " probably too small"]]; -1];
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PROG
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(Haskell)
a212813 n | n < 7 = -1
| otherwise = fst $ (until ((== 8) . snd))
(\(s, x) -> (s + 1, a036288 x)) (0, n)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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