A007547 Number of steps to compute n-th prime in PRIMEGAME (slow version).

19, 69, 281, 710, 2375, 3893, 8102, 11361, 19268, 36981, 45680, 75417, 101354, 118093, 152344, 215797, 293897, 327571, 429229, 508284, 556494, 701008, 809381, 990746, 1274952, 1435957, 1531854, 1712701, 1820085, 2021938, 2835628, 3107393, 3549288, 3723821

Offset: 1

Author

N. J. A. Sloane

Keywords

• easy
• nonn
• nice

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

• Bert Dobbelaere, Table of n, a(n) for n = 1..1000
• 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.
• R. K. Guy, Conway's prime producing machine, Math. Mag. 56 (1983), no. 1, 26-33.

Crossrefs

Cf. A007542, A007546.

Cf. A006530, A034785.

Programs

Haskell

import Data.List (elemIndices)
a007547 n = a007547_list !! n
a007547_list = tail $ elemIndices 2 $ map a006530 a007542_list
-- Reinhard Zumkeller, Jan 24 2012

Maple

a:= proc(n) option remember; local l, p, m, k;
      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, 55/1]:
      if n=1 then b(0):= 2; 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 2^ilog2(p)=p then break fi
      od:
      b(n):= p;
      m + a(n-1)
    end:
seq(a(n), n=1..10);  # Alois P. Heinz, May 01 2011

Mathematica

Clear[a]; a[n_] := a[n] = Module[{l, p, m, k}, 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, 55/1}; If[n == 1, b[0] = 2; 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[2^(Length[IntegerDigits[p, 2]]-1) == p, Break[]]]; b[n] = p; m + a[n-1]]; Table[Print[a[n]]; a[n], {n, 1, 30}] (* Jean-François Alcover, Nov 25 2014, after Alois P. Heinz *)

Extensions

More terms from Alois P. Heinz, May 01 2011