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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
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
Sequence in context: A147675 A070291 A361671 * A141321 A146266 A146218
KEYWORD
easy,look,nonn
AUTHOR
Alois P. Heinz, Dec 26 2010
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)