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A183132 Successive integers produced by Conway's PRIMEGAME using Kilminster's Fractran program with only nine fractions. 5
10, 5, 36, 858, 234, 5577, 1521, 3549, 8281, 910, 100, 50, 25, 180, 3388, 924, 252, 6006, 1638, 39039, 10647, 24843, 57967, 6370, 700, 300, 7150, 1950, 46475, 12675, 29575, 3250, 360, 6776, 1848, 504, 12012, 3276, 78078, 21294, 507507, 138411, 322959, 753571 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The exponents of exact powers of 10 in this sequence are 1, followed by the successive primes (A008578).

REFERENCES

D. Olivastro, Ancient Puzzles. Bantam Books, NY, 1993, p. 21.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10547

J. H. Conway, FRACTRAN: a simple universal programming language for arithmetic, in T. M. Cover and Gopinath, eds., Open Problems in Communication and Computation, Springer, NY 1987, pp. 4-26.

Esolang wiki, Fractran

Chaim Goodman-Strauss, Can’t Decide? Undecide!, Notices of the AMS, Volume 57, Number 3, pp. 343-356, March 2010.

R. K. Guy, Conway's prime producing machine, Math. Mag. 56 (1983), no. 1, 26-33.

Eric Weisstein's World of Mathematics, FRACTRAN.

Wikipedia, FRACTRAN.

MAPLE

l:= [3/11, 847/45, 143/6, 7/3, 10/91, 3/7, 36/325, 1/2, 36/5]:

a:= proc(n) option remember;

      global l;

      local p, k;

      if n=1 then 10

             else p:= a(n-1);

                  for k while not type(p*l[k], integer)

                  do od; p*l[k]

      fi

    end:

seq(a(n), n=1..50);

MATHEMATICA

l = {3/11, 847/45, 143/6, 7/3, 10/91, 3/7, 36/325, 1/2, 36/5};

a[n_] := a[n] = Module[{p, k}, If[n == 1, 10, p = a[n - 1]; For[k = 1, !IntegerQ[p*l[[k]]], k++]; p*l[[k]]]];

Array[a, 50] (* Jean-François Alcover, May 28 2018, from Maple *)

PROG

(Python)

from fractions import Fraction

nums = [ 3, 847, 143, 7, 10, 3,  36, 1, 36]

dens = [11,  45,   6, 3, 91, 7, 325, 2,  5]

PRIMEGAME = [Fraction(num, den) for num, den in zip(nums, dens)]

def succ(n, program):

    for i in range(len(program)):

      if (n*program[i]).denominator == 1: return (n*program[i]).numerator

def orbit(start, program, steps):

    orb = [start]

    for s in range(1, steps): orb.append(succ(orb[-1], program))

    return orb

print(orbit(10, PRIMEGAME, steps=44)) # Michael S. Branicky, Oct 05 2021

CROSSREFS

Cf. A183133, A008578, A007542, A007546, A007547.

Sequence in context: A046797 A147675 A070291 * A141321 A146266 A146218

Adjacent sequences:  A183129 A183130 A183131 * A183133 A183134 A183135

KEYWORD

easy,look,nonn

AUTHOR

Alois P. Heinz, Dec 26 2010

STATUS

approved

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Last modified October 26 02:14 EDT 2021. Contains 348256 sequences. (Running on oeis4.)