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
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
- 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
Programs
-
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 -
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 ] ] ] ]
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
Comments