A095773 a(1)=1, a(n) = 1 + a(n - a(a(a(n-1)))).

1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22

Offset: 1

Author

Benoit Cloitre, Jun 05 2004

Keywords

• nonn

Comments

A generalization of Golomb's sequence.

a(10^n): 1, 6, 26, 124, 611, 2963, 14172, ...

Links

• J. Grytczuk, Another variation on Conway's recursive sequence, Discr. Math. 282 (2004), 149-161.

Crossrefs

Cf. A001462, A095774, A095775.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = 1 + a[n - a[a[a[n - 1]]]]; Table[ a[n], {n, 80}] (* Robert G. Wilson v, Jun 09 2004 *)

PARI

v=vector(1000,j,1);for(n=2,1000,g=v[n-v[v[v[n-1]]]]+1;v[n]=g);a(n)=v[n]

Formula

Is a(n) asymptotic to r^(r-1)*n^r where r is the positive root of x^3+x=1 and so r=0.682327803828019327...?