A033958 In the '3x+1' problem, these values for the starting value set new records for number of steps to reach 1.

1, 3, 7, 9, 25, 27, 73, 97, 129, 171, 231, 313, 327, 703, 871, 1161, 2463, 2919, 3711, 6171, 10971, 13255, 17647, 23529, 26623, 34239, 35655, 52527, 77031, 106239, 142587, 156159, 216367, 230631, 410011, 511935, 626331, 837799, 1117065, 1501353, 1723519, 2298025, 3064033

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

Charles R Greathouse IV, Table of n, a(n) for n = 1..71

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

Formula

Positions of records in A006667. - Sean A. Irvine, Jul 22 2020

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 ] ] ] ] (* Winston C. Yang (winston(AT)cs.wisc.edu), Aug 27 2000 *)

Prog

(Haskell)
a033958 n = a033958_list !! (n-1)
-- For definition of a033958_list: see A033959.
-- Reinhard Zumkeller, Jan 08 2014

Crossrefs

Cf. A006884, A006885, A006877, A006878, A033492, A033959.

Sequence in context: A099886 A118564 A098338 * A352016 A018827 A249664

Adjacent sequences: A033955 A033956 A033957 * A033959 A033960 A033961

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from Jud McCranie, Jan 26 2000

Corrected with Mathematica code by Winston C. Yang (winston(AT)cs.wisc.edu), Aug 27 2000

a(40)-a(43) from Charles R Greathouse IV, Oct 07 2013

Status

approved