A033959 Record number of steps to reach 1 in '3x+1' problem, corresponding to starting values in A033958.

0, 2, 5, 6, 7, 41, 42, 43, 44, 45, 46, 47, 52, 62, 65, 66, 76, 79, 87, 96, 98, 101, 102, 103, 113, 114, 119, 125, 129, 130, 138, 141, 142, 164, 166, 174, 189, 195, 196, 197, 207, 208, 209, 217, 222, 228, 248, 256, 257, 258, 263, 278, 357, 358, 359, 362, 370

Offset

1,2

Comments

Only the 3x+1 steps, not the halving steps, are counted.

References

D. R. Hofstadter, Goedel, Escher, Bach: an Eternal Golden Braid, Random House, 1980, p. 400.

G. T. Leavens and M. Vermeulen, 3x+1 search problems, Computers and Mathematics with Applications, 24 (1992), 79-99.

Links

Table of n, a(n) for n=1..57.

Brian Hayes, Computer Recreations: On the ups and downs of hailstone numbers, Scientific American, 250 (No. 1, 1984), pp. 10-16.

Index entries for sequences from "Goedel, Escher, Bach"

Index entries for sequences related to 3x+1 (or Collatz) problem

Maple

A033959 := proc(n) local a, L; L := 0; a := n; while a <> 1 do if a mod 2 = 0 then a := a/2; else a := 3*a+1; L := L+1; fi; od: RETURN(L); end;

Mathematica

f[ nn_ ] := Module[ {c, n}, c = 0; n = nn; While[ n != 1, If[ Mod[ n, 2 ] == 0, n /= 2, n = 3*n + 1; c++ ] ]; Return[ c ] ] maxx = -1; For[ n = 1, n <= 10^8, n++, Module[ {val}, val = f[ n ]; If[ val > maxx, maxx = val; Print[ n, " ", val ] ] ] ]

Prog

(Haskell)
a033959 n = a033959_list !! (n-1)
(a033959_list, a033958_list) = unzip $ (0, 1) : f 1 1 where
   f i x | y > x     = (y, 2 * i - 1) : f (i + 1) y
         | otherwise = f (i + 1) x
         where y = a075680 i
-- Reinhard Zumkeller, Jan 08 2014

Crossrefs

Cf. A006884, A006885, A006877, A006878, A033492, A033958.

Cf. A075680.

Sequence in context: A346880 A344865 A350130 * A167455 A159752 A352325

Adjacent sequences: A033956 A033957 A033958 * A033960 A033961 A033962

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from Winston C. Yang (winston(AT)cs.wisc.edu), Aug 27 2000

More terms from Larry Reeves (larryr(AT)acm.org), Sep 27 2000

Offset corrected by Reinhard Zumkeller, Jan 08 2014

Status

approved