A320063 A sequence which changes by one or zero: a(n) = a(n-1-a(a(n-1))) + a(a(a(n-1))) for n > 1, a(n) = n for n < 2.

0, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7, 8, 8, 8, 8, 9, 10, 10, 10, 10, 11, 12, 12, 13, 13, 13, 13, 14, 15, 15, 15, 16, 17, 17, 17, 17, 18, 19, 19, 19, 20, 20, 21, 21, 21, 21, 21, 22, 23, 23, 23, 24, 24, 25, 26, 27, 27, 27, 27, 27, 28, 28, 29, 29, 29

Offset: 0

Author

David S. Newman, Oct 04 2018

Keywords

• nonn

Comments

This is similar to a problem that I had in the Monthly 35 years ago. The solution then was by Daniel Kleitman.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..65535
• Abraham Isgur, Mustazee Rahman, On variants of Conway and Conolly's Meta-Fibonacci recursions, arXiv:1407.0425 [math.CO], 2014.
• T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252.
• David Newman and Daniel J. Kleitman, Solution to Problem E3274, Amer. Math. Monthly, 98 (1991), 958-959.

Crossrefs

Cf. A093878.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, n,
      a(n-1-a(a(n-1)))+a(a(a(n-1))))
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Oct 08 2018

Mathematica

f[0] = 0;
f[1] = 1;
f[n_] := f[n] = +f[n - 1 - f[f[n - 1]]] + f[f[f[n - 1]]];
Table[f[i], {i, 1, 30}]