A007546 Number of steps to compute n-th prime in PRIMEGAME (fast version). (Formerly M5074)

19, 69, 280, 707, 2363, 3876, 8068, 11319, 19201, 36866, 45551, 75224, 101112, 117831, 152025, 215384, 293375, 327020, 428553, 507519, 555694, 700063, 808331, 989526, 1273490, 1434366, 1530213, 1710923, 1818254, 2019962, 2833089, 3104685, 3546320, 3720785

Offset

1,1

Comments

The FRACTRAN program considered here is (17/91, 78/85, 19/51, 23/38, 29/33, 77/29, 95/23, 77/19, 1/17, 11/13, 13/11, 15/14, 15/2, 55/1), which differs slightly from that used in A007547. - Pontus von Brömssen, Apr 30 2026

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..5000

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.

OEIS Wiki, Conway's PRIMEGAME.

Wikipedia, FRACTRAN.

Maple

with(numtheory): f:= proc(n) local l, b, d; l:= sort([divisors (n)[]]); b:= l[nops(l)-1]; n-1 +(6*n+2)*(n-b) +2*add(floor(n/d), d=b..n-1) end: a:= proc(n) option remember; `if`(n=1, f(2), a(n-1) +add(f(i), i=ithprime(n-1)+1..ithprime(n))) end: seq(a(n), n=1..40); # Alois P. Heinz, Aug 12 2009

Mathematica

f[n_] := Module[{l, b, d}, l = Divisors [n]; b = l[[-2]]; n-1 + (6*n+2)*(n-b) + 2*Sum[Floor[n/d], {d, b, n-1}]]; a[n_] := a[n] = If[n == 1, f[2], a[n-1] + Sum[f[i], {i, Prime[n-1]+1, Prime[n]}]]; Table[a[n], {n, 1, 32}] (* Jean-François Alcover, Oct 04 2013, translated from Alois P. Heinz's Maple program *)

Crossrefs

Cf. A007542, A007547.

Sequence in context: A300463 A204675 A382973 * A007547 A217081 A010007

Adjacent sequences: A007543 A007544 A007545 * A007547 A007548 A007549

Keyword

easy,nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from Alois P. Heinz, Aug 12 2009

Status

approved