A350663 Numerators of Conway's POLYGAME.

583, 629, 437, 82, 615, 371, 1, 53, 43, 23, 341, 41, 47, 29, 37, 37, 299, 47, 161, 527, 159, 1, 1, 1

Offset

1,1

Comments

These rational numbers represent a FRACTRAN program capable of calculating any computable function.

If, when started at c*2^(2^k), the program stops at 2^(2^m), then c encodes the computable function f_c, and f_c(k) = m, where c, k and m are nonnegative integers.

In the linked work Conway lists some values of c (which he calls "catalog numbers") encoding various simple functions, including the (extremely large) value of c for computing the k-th digit in the decimal expansion of Pi.

Links

Table of n, a(n) for n=1..24.

J. H. Conway, "FRACTRAN: A Simple Universal Programming Language for Arithmetic", in T. M. Cover and B. Gopinath, eds, Open Problems in Communication and Computation, Springer, New York, NY, 1987, pp. 4-26.

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, pp. 249-264.

Wikipedia, FRACTRAN.

Crossrefs

Cf. A202138, A350555, A350664 (denominators).

Sequence in context: A162705 A244344 A059468 * A122694 A032373 A236486

Adjacent sequences: A350660 A350661 A350662 * A350664 A350665 A350666

Keyword

nonn,frac,fini,full

Author

Paolo Xausa, Jan 10 2022

Status

approved