A153112 a(0) = 0 and a(1)=a(2)=1; a(n) = a(a(n-1)) + a(n-a(n-1)) unless floor( sum_{i=0..n-1} a(i)/2) mod 16*A069705(n) = 1 in which case a(n) = A010882(n).

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

Offset: 0

Author

Roger L. Bagula, Dec 18 2008

Keywords

• nonn

References

• Per Bak, "How nature works, the science of self-organized criticality", Springer, New York (1996), pp. 49-64.

Crossrefs

Cf. A004001, A092550, A136640.

Programs

Maple

A069705 := proc(n) op(1+(n mod 3), [1,2,4]) ; end proc:
A010882 := proc(n) op(1+(n mod 3), [1,2,3]) ; end proc:
A153112 := proc(n) option remember; local psu ; if n=0 then 0; elif n<=2 then 1; else psu := add( procname(i),i=0..n-1) ; if floor(psu/2) mod (16*A069705(n)) = 1 then A010882(n) ; else procname(procname(n-1)) +procname(n-procname(n-1)) ; end if; end if; end proc:
seq(A153112(n),n=0..100) ; # R. J. Mathar, Jun 24 2011

Mathematica

Clear[f, n]; f[0] = 0; f[1] = 1; f[2] = 1;
f[n_] := f[n] = If[Mod[ Floor[Sum[f[i], {i,0, n - 1}]/2], 2^(4 + Mod[n, 3])] == 1, 1 + Mod[n, 3],
f[f[n - 1]] + f[n - f[n - 1]]]; a = Table[f[n], {n, 0, 200}]

Extensions

Definition cleaned up. - R. J. Mathar, Jun 24 2011