A212813 Number of steps for n to reach 8 under iteration of the map i -> A036288(i), or -1 if 8 is never reached.

-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

Offset: 1

Author

N. J. A. Sloane, May 30 2012

Keywords

• sign

Comments

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.

a(A212911(n)) = n and a(m) < n for m < A212911(n). - Reinhard Zumkeller, May 30 2012

References

• 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.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A036288, A212814, A212815, A212816, A212908, A212909, A212911.

Programs

Haskell

a212813 n | n < 7     = -1
          | otherwise = fst $ (until ((== 8) . snd))
                              (\(s, x) -> (s + 1, a036288 x)) (0, n)
-- Reinhard Zumkeller, May 30 2012

Maple

Simple-minded Maple program from N. J. A. Sloane, May 30 2012:
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

Mathematica

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];
Array[a, 120] (* Jean-François Alcover, Aug 01 2018 *)

PARI

A212813(n)={ n>8 & for(c=1,9e9,(n=A036288(n))==8 & return(c));(n==7)-(n<7) }  \\ M. F. Hasler, May 30 2012