

A062054


Numbers with 4 odd integers in their Collatz (or 3x+1) trajectory.


7



17, 34, 35, 68, 69, 70, 75, 136, 138, 140, 141, 150, 151, 272, 276, 277, 280, 282, 300, 301, 302, 544, 552, 554, 560, 564, 565, 600, 602, 604, 605, 1088, 1104, 1108, 1109, 1120, 1128, 1130, 1137, 1200, 1204, 1205, 1208, 1210, 2176, 2208, 2216, 2218, 2240
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OFFSET

1,1


COMMENTS

The Collatz (or 3x+1) function is f(x) = x/2 if x is even, 3x+1 if x is odd.
The Collatz trajectory of n is obtained by applying f repeatedly to n until 1 is reached.
Numbers m such that (s0  4s1)/2m = 1 where s0 is the sum of the even elements and s1 the sum of the odd elements in the Collatz trajectory of m.  Michel Lagneau, Aug 13 2018
If m is in the sequence then so is 2*m, so one would only have to check odd numbers.  David A. Corneth, Aug 13 2018


REFERENCES

J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182185.


LINKS



FORMULA

The twelve formulas giving this sequence are listed in Corollary 3.3 in J. R. Goodwin with the following caveats: the value x cannot equal zero in formulas (3.16) and (3.20), one must multiply the formulas by all powers of 2 (2^1, 2^2, ...) to get the evens.  Jeffrey R. Goodwin, Oct 26 2011


EXAMPLE

The Collatz trajectory of 17 is (17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1), which contains 4 odd integers.  Jeffrey R. Goodwin, Oct 26 2011


MATHEMATICA

col4Q[n_]:=Module[{c=NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #!=1&]}, Count[c, _?OddQ]==4]; Select[Range[2500], col4Q] (* Harvey P. Dale, Mar 21 2011 *)


PROG

(Haskell)
import Data.List (elemIndices)
a062054 n = a062054_list !! (n1)
a062054_list = map (+ 1) $ elemIndices 4 a078719_list


CROSSREFS

Cf. A000079, A006370, A062052, A062053, A062055, A062056, A062057, A062058, A062059, A062060, A092893, A198587.


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



