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A033958
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In the '3x+1' problem, these values for the starting value set new records for number of steps to reach 1.
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5
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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
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OFFSET
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1,2
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COMMENTS
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Only the 3x+1 steps, not the halving steps, are counted.
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REFERENCES
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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.
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LINKS
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FORMULA
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
a033958 n = a033958_list !! (n-1)
-- For definition of a033958_list: see A033959.
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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Corrected with Mathematica code by Winston C. Yang (winston(AT)cs.wisc.edu), Aug 27 2000
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STATUS
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approved
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