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

1,3

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

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]

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 *)

Crossrefs

Cf. A004001, A005185.

Sequence in context: A006949 A359536 A194814 * A284520 A369057 A342248

Adjacent sequences: A055745 A055746 A055747 * A055749 A055750 A055751

Keyword

nonn,look

Author

N. J. A. Sloane, Jul 13 2000

Status

approved