A093878 a(1)=a(2)=1; for n >=3, a(n) = a(a(a(n-1))) + a(n-a(a(n-1))).

1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 11, 12, 12, 12, 13, 13, 14, 15, 16, 16, 17, 18, 19, 20, 20, 20, 20, 21, 21, 22, 23, 24, 25, 26, 27, 27, 28, 28, 28, 29, 30, 31, 32, 33, 33, 33, 33, 33, 34, 34, 35, 36, 37, 38, 38, 39, 40, 41, 42, 43, 44, 45, 46, 46, 47, 47, 47, 48, 48

Offset: 1

Author

N. J. A. Sloane, May 27 2004

Keywords

• nonn
• easy

Comments

For n>1: a(n)A001519 where phi is the golden ratio = (1+sqrt(5))/2 - Benoit Cloitre, May 27 2004

Links

• J. Grytczuk, Another variation on Conway's recursive sequence, Discr. Math. 282 (2004), 149-161.
• Abraham Isgur, Mustazee Rahman, On variants of Conway and Conolly's Meta-Fibonacci recursions, arXiv:1407.0425 [math.CO], 2014.

Programs

Mathematica

a[1] = a[2] = 1; a[n_] := a[n] = a[a[a[n - 1]]] + a[n - a[a[n - 1]]]; Table[ a[n], {n, 75}] (* Robert G. Wilson v, May 27 2004 *)

PARI

{m=75;v=vector(m,j,1);for(n=3,m,a=v[v[v[n-1]]]+v[n-v[v[n-1]]];v[n]=a);for(j=1,m,print1(v[j],","))} \\ Klaus Brockhaus, May 27 2004

Formula

a(A001519(n)) = floor((phi-1)*A001519(n)); a(A000045(n)) = A000045(n-1); liminf a(n)/n = phi-1; limsup a(n)/n = ? - Benoit Cloitre, May 27 2004

Extensions

More terms from Benoit Cloitre, Robert G. Wilson v and Klaus Brockhaus, May 27 2004