A365328 Numerators of a FRACTRAN program that produces the iterates of the Collatz (or 3x+1) function.

1, 136, 5, 4, 26, 7, 1, 33, 5, 7

Offset

1,2

Comments

These rational numbers (denominators are in A365329) represent a FRACTRAN program that, when started at 2^m, will produce 2^T(m) as the next power of 2, where T(m) is the Collatz or 3x+1 function = (3m+1)/2 if m is odd, m/2 if m is even (A014682).

Monks (2002) uses this program to prove Theorem 1 in his paper.

Links

Table of n, a(n) for n=1..10.

J. H. Conway, "FRACTRAN: A Simple Universal Programming Language for Arithmetic", in J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, American Mathematical Society, 2010, p. 249, and in T. M. Cover and B. Gopinath, eds, Open Problems in Communication and Computation, Springer, New York, NY, 1987, pp. 4-26.

J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, American Mathematical Society, 2010, p. 110.

Kenneth G. Monks, 3x+1 Minus the +, Discrete Mathematics and Theoretical Computer Science, 2002, Vol. 5, pp. 47-54.

Wikipedia, FRACTRAN.

Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A014682, A365329 (denominators).

Sequence in context: A051307 A056740 A065663 * A269062 A270301 A281241

Adjacent sequences: A365325 A365326 A365327 * A365329 A365330 A365331

Keyword

nonn,frac,fini,full

Author

Paolo Xausa, Sep 01 2023

Status

approved