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 A125731 a(n) = minimal number of steps to get from 1 to n, where a step is x -> 3x+1 if x is odd, or x -> either x/2 or 3x+1 if x is even. Set a(n) = -1 if n cannot be reached from 1. 3
 0, 2, -1, 1, 6, -1, 3, 8, -1, 5, 5, -1, 2, 15, -1, 7, 7, -1, 12, 4, -1, 4, 9, -1, 9, 9, -1, 14, 14, -1, 6, 19, -1, 6, 11, -1, 11, 11, -1, 3, 29, -1, 16, 16, -1, 8, 8, -1, 8, 21, -1, 8, 13, -1, 26, 13, -1, 13, 13, -1, 5, 31, -1, 18, 18, -1, 5, 23, -1, 10 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In contrast to the "3x+1" problem, here you are free to choose either step if x is even. Clearly a(3k) = -1 for all k; we conjecture that a(n) >= 0 otherwise. See A127885 for the number of steps in the reverse direction, from n to 1. LINKS David Applegate, Table of n, a(n) for n = 1..1000 EXAMPLE The initial values use these paths: 1 -> 4 -> 2 -> 7 -> 22 -> 11. 1 -> 4 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8. 1 -> 4 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 49 -> 148 -> 74 -> 37 -> 12 -> 56 -> 28 -> 14. MAPLE # Code from David Applegate: Be careful - the function takes an iteration limit and returns the limit if it wasn't able to determine the answer (that is, if A125731(n, lim) == lim, all you know is that the value is >= lim). To use it, do manual iteration on the limit. A125731 := proc(n, lim) local d, d2; options remember; if (n = 1) then return 0; end if; if (n mod 3 = 0) then return -1; end if; if (lim <= 0) then return 0; end if; if (n > (3 ** (lim+1) - 1)/2) then return lim; end if; if (n mod 9 = 4 or n mod 9 = 7) then d := A125731((n-1)/3, lim-1); d2 := A125731(2*n, d); if (d2 < d) then d := d2; end if; else d := A125731(2*n, lim-1); end if; return 1+d; end proc; CROSSREFS Sequence in context: A053383 A181538 A322128 * A123361 A265315 A179380 Adjacent sequences:  A125728 A125729 A125730 * A125732 A125733 A125734 KEYWORD sign AUTHOR David Applegate and N. J. A. Sloane, Feb 02 2007 STATUS approved

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Last modified November 22 16:13 EST 2019. Contains 329396 sequences. (Running on oeis4.)