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 A220071 Difference between number of halving steps and number of tripling steps needed to reach 1 in '3x+1' problem. 3
 0, 1, 3, 2, 3, 4, 6, 3, 7, 4, 6, 5, 5, 7, 7, 4, 6, 8, 8, 5, 5, 7, 7, 6, 9, 6, 29, 8, 8, 8, 28, 5, 10, 7, 7, 9, 9, 9, 12, 6, 29, 6, 11, 8, 8, 8, 28, 7, 10, 10, 10, 7, 7, 30, 30, 9, 12, 9, 12, 9, 9, 29, 29, 6, 11, 11, 11, 8, 8, 8, 28, 10, 31, 10, 8, 10, 10, 13 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This sequence can also be defined as: a(1) = 0; thereafter a(2*k) = a(k) + 1, a(2*k+1) = a(6*k+4) - 1. - Gionata Neri, Jul 17 2016 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A006666(n) - A006667(n). MAPLE a:= proc(n) option remember; `if`(n<2, 0, `if`(irem(n, 2)=0, 1+a(n/2), a((3*n+1)/2))) end: seq(a(n), n=1..100); # Alois P. Heinz, Feb 19 2013 MATHEMATICA coll[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[(x = Count[coll[n], _?EvenQ]) - (Length[coll[n]] - x - 1), {n, 78}] (* Jayanta Basu, Aug 15 2013 *) CROSSREFS Cf. A006577, A006666, A006667, A014682. Sequence in context: A035366 A114751 A211947 * A132408 A091821 A086035 Adjacent sequences: A220068 A220069 A220070 * A220072 A220073 A220074 KEYWORD nonn AUTHOR Jayanta Basu, Feb 19 2013 EXTENSIONS More terms from Alois P. Heinz, Feb 19 2013 STATUS approved

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Last modified September 17 05:28 EDT 2024. Contains 375985 sequences. (Running on oeis4.)