



1, 2, 3, 4, 5, 7, 8, 8, 11, 10, 12, 14, 14, 16, 16, 16, 18, 22, 22, 21, 21, 25, 25, 28, 29, 28, 32, 33, 33, 33, 36, 32, 39, 37, 37, 44, 44, 44, 47, 42, 48, 42, 53, 50, 50, 50, 54, 56, 59, 59, 59, 56, 56, 64, 64, 67, 71, 67, 71, 67, 67, 72, 72, 64, 79, 79, 79, 75
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OFFSET

1,2


COMMENTS

The sequence contains A211981 and the powers of 2 (A000079).
There exists a subset E = { 1, 2, 3, 4, 5, 8, 10, 16, 21, 32, 42, 64, 85, 128, 170, 227, 256, 341, 512, 682, 1024, 2048, ...} in {a(n)} such that each element m of E generates the Collatz sequence of iterates m > T_1(m) > T_2(m) > T_3(m) > ... > 1 where any T_i(m) is an element of E of the form [2^i /3^j] where i = A006666(m), or A006666(m)1, or ... and j = A006667(m), or A006667(m)1, or ..., but with A006667(m) <= 3. If m is even then m/2 is in E.
For example, the statement that "3 is an element of E" implies that each element of the trajectory 3 > 10 > 5 > 16 > 8 > 4 > 2 > 1 belongs to E. Thus the trajectory of the number 3 can be represented by [2^5/3^2] > [2^5/3^1] > [2^4/3^1] > [2^4/3^0] > [2^3/3^0] > [2^2/3^0] > [2^1/3^0] > [2^0/3^0].


LINKS

Table of n, a(n) for n=1..68.
Index entries for sequences related to 3x+1 (or Collatz) problem


EXAMPLE

a(39) = [2^A006666(39)/3^A006667(39)] = [2^23/3^11] = [47.353937...] = 47.


MATHEMATICA

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 70; t = {}; n = 0; While[Length[t] < nn, n++; c = Collatz[n]; ev = Length[Select[c, EvenQ]]; od = Length[c]  ev  1; AppendTo[t, Floor[2^ev/3^od]]]; t


PROG

(PARI) a(n) = my(t, h); while(n>1, if(n%2, n=3*n+1; t++, n>>=1; h++)); 2^h\3^t; \\ Michel Marcus, May 05 2018


CROSSREFS

Cf. A000079, A006666, A006667, A211981, A225089, A265099.
Sequence in context: A107900 A112922 A305077 * A228683 A133017 A290019
Adjacent sequences: A302172 A302173 A302174 * A302176 A302177 A302178


KEYWORD

nonn,easy


AUTHOR

Michel Lagneau, Apr 03 2018


STATUS

approved



