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A212813 Number of steps for n to reach 8 under iteration of the map i -> A036288(i), or -1 if 8 is never reached. 8
-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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

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

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

PROG

(Haskell)

a212813 n | n < 7     = -1

          | otherwise = fst $ (until ((== 8) . snd))

                              (\(s, x) -> (s + 1, a036288 x)) (0, n)

-- Reinhard Zumkeller, May 30 2012

(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

CROSSREFS

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

Sequence in context: A029327 A079135 A271315 * A112219 A035458 A259771

Adjacent sequences:  A212810 A212811 A212812 * A212814 A212815 A212816

KEYWORD

sign

AUTHOR

N. J. A. Sloane, May 30 2012

STATUS

approved

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Last modified November 21 13:53 EST 2017. Contains 295001 sequences.