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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 + A007546. - 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

Alois P. Heinz, Table of n, a(n) for n=1..8103

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.

Eric Weisstein's World of Mathematics, FRACTRAN

Wikipedia, Conway's PRIMEGAME

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-Fran├žois 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

CROSSREFS

Cf. A007546, A007547, A183132, A202138, A203363.

Sequence in context: A012993 A216331 A179432 * A090604 A007467 A132317

Adjacent sequences:  A007539 A007540 A007541 * A007543 A007544 A007545

KEYWORD

easy,nonn,look,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 19 01:29 EDT 2017. Contains 290787 sequences.