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

Author

N. J. A. Sloane

Keywords

• nonn
• nice

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

Crossrefs

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

Programs

Haskell

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

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 *)

Formula

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

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