login
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
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
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
KEYWORD
easy,look,nonn
AUTHOR
Alois P. Heinz, Dec 26 2010
STATUS
approved