A083417 Primitive recursive function r(z, r(s, r(s, r(s, p_2)))) at (n, 0).

0, 1, 2, 1, 0, 5, 2, 3, 3, 2, 2, 3, 4, 1, 8, 5, 4, 2, 2, 3, 3, 2, 2, 7, 2, 9, 5, 2, 12, 9, 7, 5, 4, 2, 2, 3, 4, 1, 8, 5, 4, 2, 2, 3, 3, 2, 2, 15, 8, 5, 1, 43, 20, 13, 10, 3, 14, 7, 3, 11, 8, 3, 8, 5, 4, 2, 2, 3, 4, 1, 24, 13, 5, 4, 2, 11, 4, 5, 5, 4, 1, 13, 6, 5, 5, 4, 2, 7, 5, 3, 1, 3, 3, 2, 2, 31, 14, 10, 3

Offset: 0

Author

Alex Fink, Jun 08 2003

Keywords

• nonn

References

• S. Wolfram, A New Kind of Science, 2001, p. 908.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000
• S. Wolfram, A New Kind of Science, pages 907-908.

Crossrefs

A253099 gives locations of zeros.

Programs

Maple

z := x -> 0: s := x -> (1 + op(1, x)): p := x -> subs(q = x, y -> op(q, y)): c := x -> subs(q = x, y -> eval((op(1, q))([(seq(op(i, q), i = 2..nops(q)))(y)]))): r := x -> subs(q = x, y -> eval(`if`(op(1, y) = 0, (op(1, q))([op(2, y)]), (op(2, q))([r(q)([op(1, y) - 1, op(2, y)]), op(1, y) - 1, op(2, y)])))): seq(r([z, r([s, r([s, r([s, p(2)])])])])([i, 0]), i = 0..109);

Mathematica

(* Mathematica code from New Kind of Science, p. 908, added by N. J. A. Sloane, Feb 17 2015 *)
F = Fold[Fold[
     2^Ceiling[Log[2, Ceiling[(#1 + 2)/(#2 + 2)]]] (#2 + 2) -
       2 - #1 &, #2, Range[#1]] &, 0, Range[#]] &
Table[F[n], {n, 0, 98}]

PARI

f(x,y)=(y+2)<Charles R Greathouse IV, Jan 25 2012