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A007542 Successive integers produced by Conway's PRIMEGAME.
(Formerly M2084)
13
2, 15, 825, 725, 1925, 2275, 425, 390, 330, 290, 770, 910, 170, 156, 132, 116, 308, 364, 68, 4, 30, 225, 12375, 10875, 28875, 25375, 67375, 79625, 14875, 13650, 2550, 2340, 1980, 1740, 4620, 4060, 10780, 12740, 2380, 2184, 408, 152 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Conway's PRIMEGAME produces the terms 2^prime in increasing order.
From Daniel Forgues, Jan 20 2016: (Start)
Pairs (n, a(n)) such that a(n) = 2^k are (1, 2^1), (20, 2^2), (70, 2^3), (282, 2^5), (711, 2^7), (2376, 2^11), (3894, 2^13), (8103, 2^17), ...
Numbers n such that a(n) = 2^k are 1, 20, 70, 282, 711, 2376, 3894, 8103, ... [This is 1 + A007547. - N. J. A. Sloane, Jan 25 2016] (End)
REFERENCES
D. Olivastro, Ancient Puzzles. Bantam Books, NY, 1993, p. 21.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
Richard K. Guy, Conway's prime producing machine, Math. Mag. 56 (1983), no. 1, 26-33. [Gives slightly different version of the program which produces different terms, starting from n=132.]
Kevin I. Piterman and Leandro Vendramin, Computer algebra with GAP, 2023. See p. 40.
Leandro Vendramin, Mini-couse on GAP - Exercises, Universidad de Buenos Aires (Argentina, 2020).
Eric Weisstein's World of Mathematics, FRACTRAN
Wikipedia, FRACTRAN
FORMULA
a(n+1) = A203907(a(n)), a(1) = 2. [Reinhard Zumkeller, Jan 24 2012]
MAPLE
l:= [17/91, 78/85, 19/51, 23/38, 29/33, 77/29, 95/23, 77/19, 1/17, 11/13, 13/11, 15/2, 1/7, 55]: a:= proc(n) option remember; global l; local p, k; if n=1 then 2 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); # Alois P. Heinz, Aug 12 2009
MATHEMATICA
conwayFracs := {17/91, 78/85, 19/51, 23/38, 29/33, 77/29, 95/23, 77/19, 1/17, 11/13, 13/11, 15/2, 1/7, 55}; a[1] = 2; A007542[n_] := A007542[n] = (p = A007542[n - 1]; k = 1; While[ ! IntegerQ[p * conwayFracs[[k]]], k++]; p * conwayFracs[[k]]); Table[A007542[n], {n, 42}] (* Jean-François Alcover, Jan 23 2012, after Alois P. Heinz *)
PROG
(Haskell)
a007542 n = a007542_list !! (n-1)
a007542_list = iterate a203907 2 -- Reinhard Zumkeller, Jan 24 2012
(Python)
from fractions import Fraction
nums = [17, 78, 19, 23, 29, 77, 95, 77, 1, 11, 13, 15, 1, 55] # A202138
dens = [91, 85, 51, 38, 33, 29, 23, 19, 17, 13, 11, 2, 7, 1] # A203363
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(2, PRIMEGAME, steps=42)) # Michael S. Branicky, Feb 15 2021
CROSSREFS
Sequence in context: A012993 A216331 A179432 * A090604 A007467 A132317
KEYWORD
easy,nonn,look,nice
AUTHOR
STATUS
approved

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Last modified March 19 02:55 EDT 2024. Contains 370952 sequences. (Running on oeis4.)