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

10, 46, 196, 500, 1428, 2488, 4588, 6840, 10546, 17118, 23064, 33332, 44472, 55848, 70330, 90836, 115136, 137912, 168802, 201000, 233542, 276680, 320332, 373198, 439722, 503810, 568334, 640092, 712314, 792186, 917090, 1023878, 1146632, 1263818, 1419298

Offset

1,1

References

D. Olivastro, Ancient Puzzles. Bantam Books, NY, 1993, p. 21.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..100

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

a:= proc(n) option remember;
      local l, p, m, k;
      l:= [3/11, 847/45, 143/6, 7/3, 10/91, 3/7, 36/325, 1/2, 36/5]:
      if n=1 then b(0):= 10; a(0):= 0
             else a(n-1)
      fi;
      p:= b(n-1);
      for m do
         for k while not type(p*l[k], integer)
         do od; p:= p*l[k];
         if 10^ilog10(p)=p then break fi
      od:
      b(n):= p;
      m + a(n-1)
    end:
seq(a(n), n=1..20);

Mathematica

a[n_] := a[n] = Module[{l, p, m, k},
     l = {3/11, 847/45, 143/6, 7/3, 10/91, 3/7, 36/325, 1/2, 36/5};
     If[n == 1, b[0] = 10; a[0] = 0, a[n - 1]]; p = b[n - 1];
     For[m = 1, True, m++,
          For[k = 1, !IntegerQ[p*l[[k]]], k++];
          p = p*l[[k]]; If[10^(Length@IntegerDigits[p]-1) == p, Break[]]];
     b[n] = p; m + a[n - 1]];
Array[a, 20] (* Jean-François Alcover, Apr 02 2021, after Alois P. Heinz *)

Crossrefs

Cf. A183132, A008578, A007542, A007546, A007547.

Sequence in context: A003197 A096045 A287090 * A115712 A199313 A003765

Adjacent sequences: A183130 A183131 A183132 * A183134 A183135 A183136

Keyword

easy,nonn

Author

Alois P. Heinz, Dec 26 2010

Status

approved