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A203907
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Successor function for Conway's PRIMEGAME.
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3
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55, 15, 165, 30, 275, 45, 1, 60, 495, 75, 13, 90, 11, 105, 825, 120, 1, 135, 77, 150, 3, 26, 95, 180, 1375, 22, 1485, 210, 77, 225, 1705, 240, 29, 2, 5, 270, 2035, 23, 33, 300, 2255, 315, 2365, 52, 2475, 190, 2585, 360, 7, 375, 19, 44, 2915, 405, 65, 420
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OFFSET
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1,1
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COMMENTS
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a(n) <= 55 * n, as 55/1 is the last and largest FRACTRAN fraction;
iterations, starting with 2, give A007542; A185242 begins with 3.
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, FRACTRAN
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FORMULA
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Let [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, 55/1] be the list of FRACTRAN fractions = [A202138(k)/A203363(k) : 1<=k<=14], then a(n) = n*f, where f is the first term yielding an integral product.
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MATHEMATICA
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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}; conwayProc[n_] := Module[{curr = 1/2, iter = 1}, While[Not[IntegerQ[curr]], curr = conwayFracs[[iter]]n; iter++]; Return[curr]]; Table[conwayProc[n], {n, 60}] (* Alonso del Arte, Jan 24 2012 *)
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PROG
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(Haskell)
import Data.Ratio ((%), numerator, denominator)
a203907 n = numerator $ head
[x | x <- map (* fromInteger n) fracts, denominator x == 1]
where fracts = zipWith (%) a202138_list a203363_list
a203907_list = map a203907 [1..]
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CROSSREFS
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Cf. A007542.
Sequence in context: A182119 A057965 A083516 * A220134 A178509 A033375
Adjacent sequences: A203904 A203905 A203906 * A203908 A203909 A203910
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Reinhard Zumkeller, Jan 24 2012
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STATUS
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approved
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