A022446 Fractal sequence of the dispersion of the composite numbers.

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

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

References

• C. Kimberling, Fractal sequences and interspersions, Ars Combinatoria, vol. 45 p 157 1997.

Links

• C. Kimberling, Interspersions

Programs

Mathematica

compositePi[n_] := Length[Select[Table[FixedPoint[i + PrimePi[#] + 1 &, i + PrimePi[i] + 1], {i,n}], # <= n &]]; compositefractal[n_] :=  PrimePi[NestWhile[compositePi, n, ! PrimeQ[#] && # != 1 &]] + 1; Array[compositefractal, 30] (* Birkas Gyorgy, Apr 05 2011 *)