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A183133 Number of steps to compute the n-th prime in PRIMEGAME using Kilminster's Fractran program with only nine fractions.

%I A183133 #30 Feb 16 2025 08:33:13
%S A183133 10,46,196,500,1428,2488,4588,6840,10546,17118,23064,33332,44472,
%T A183133 55848,70330,90836,115136,137912,168802,201000,233542,276680,320332,
%U A183133 373198,439722,503810,568334,640092,712314,792186,917090,1023878,1146632,1263818,1419298
%N A183133 Number of steps to compute the n-th prime in PRIMEGAME using Kilminster's Fractran program with only nine fractions.
%D A183133 D. Olivastro, Ancient Puzzles. Bantam Books, NY, 1993, p. 21.
%H A183133 Alois P. Heinz, <a href="/A183133/b183133.txt">Table of n, a(n) for n = 1..100</a>
%H A183133 J. H. Conway, <a href="http://dx.doi.org/10.1007/978-1-4612-4808-8_2">FRACTRAN: a simple universal programming language for arithmetic</a>, in T. M. Cover and Gopinath, eds., Open Problems in Communication and Computation, Springer, NY 1987, pp. 4-26.
%H A183133 Esolang wiki "<a href="http://www.esolangs.org/wiki/Fractran">Fractran</a>".
%H A183133 Chaim Goodman-Strauss, <a href="http://www.ams.org/notices/201003/rtx100300343p.pdf">Can’t Decide? Undecide!</a>, Notices of the AMS, Volume 57, Number 3, pp. 343-356, March 2010.
%H A183133 R. K. Guy, <a href="http://www.jstor.org/stable/2690263">Conway's prime producing machine</a>, Math. Mag. 56 (1983), no. 1, 26-33.
%H A183133 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FRACTRAN.html">FRACTRAN</a>.
%H A183133 Wikipedia, <a href="https://en.wikipedia.org/wiki/FRACTRAN">FRACTRAN</a>.
%p A183133 a:= proc(n) option remember;
%p A183133       local l,p,m,k;
%p A183133       l:= [3/11, 847/45, 143/6, 7/3, 10/91, 3/7, 36/325, 1/2, 36/5]:
%p A183133       if n=1 then b(0):= 10; a(0):= 0
%p A183133              else a(n-1)
%p A183133       fi;
%p A183133       p:= b(n-1);
%p A183133       for m do
%p A183133          for k while not type(p*l[k], integer)
%p A183133          do od; p:= p*l[k];
%p A183133          if 10^ilog10(p)=p then break fi
%p A183133       od:
%p A183133       b(n):= p;
%p A183133       m + a(n-1)
%p A183133     end:
%p A183133 seq(a(n), n=1..20);
%t A183133 a[n_] := a[n] = Module[{l, p, m, k},
%t A183133      l = {3/11, 847/45, 143/6, 7/3, 10/91, 3/7, 36/325, 1/2, 36/5};
%t A183133      If[n == 1, b[0] = 10; a[0] = 0, a[n - 1]]; p = b[n - 1];
%t A183133      For[m = 1, True, m++,
%t A183133           For[k = 1, !IntegerQ[p*l[[k]]], k++];
%t A183133           p = p*l[[k]];If[10^(Length@IntegerDigits[p]-1) == p, Break[]]];
%t A183133      b[n] = p; m + a[n - 1]];
%t A183133 Array[a, 20] (* _Jean-François Alcover_, Apr 02 2021, after _Alois P. Heinz_ *)
%Y A183133 Cf. A183132, A008578, A007542, A007546, A007547.
%K A183133 easy,nonn
%O A183133 1,1
%A A183133 _Alois P. Heinz_, Dec 26 2010