A055748 A chaotic cousin of the Hofstadter-Conway sequence A004001.

1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 7, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 11, 13, 15, 15, 14, 15, 16, 16, 16, 16, 16, 16, 16, 17, 18, 18, 18, 18, 18, 19, 21, 23, 21, 20, 24, 25, 26, 28, 27, 26, 30, 30, 29, 30, 30, 30, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 33

Offset: 1

Author

N. J. A. Sloane, Jul 13 2000

Keywords

• nonn
• look

Comments

See FORMULA for definition.

References

• S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 129.

Links

• Martin Møller Skarbiniks Pedersen, Table of n, a(n) for n = 1..10000
• J. Grytczuk, Another variation on Conway's recursive sequence, Discr. Math. 282 (2004), 149-161.
• Martin Møller Skarbiniks Pedersen, Plot of first 100000000 values (pdf)
• Martin Møller Skarbiniks Pedersen, Plot of a(n)/n for the first 100000000 values (pdf)
• Martin Møller Skarbiniks Pedersen, Plot of a(n) for the first 100,000,000 values (png)
• Martin Møller Skarbiniks Pedersen, Plot of a(n)/n for the first 100000000 values (png)
• K. Pinn, A chaotic cousin of Conway's recursive sequence, Experimental Mathematics, 9:1 (2000), 55-65.
• Index entries for Hofstadter-type sequences

Crossrefs

Cf. A004001, A005185.

Programs

Maple

A055748 := proc(n) option remember; if n<=2 then 1 else A055748(A055748(n-1))+A055748(n-1-A055748(n-2)); fi; end;

Mathematica

a[n_] := a[n] = If[n < 3, 1, a[a[n - 1]] + a[n - a[n - 2] - 1]]; Array[a, 70] (* Michael De Vlieger, Mar 29 2017 *)

Formula

a(1) = 1, a(2) = 1, a(n) = a(a(n-1)) + a(n - a(n-2) - 1) for n >= 3. [Jaroslav Krizek, Dec 09 2009]