A308004 a(n) = smallest nonnegative number that requires n applications of the Sisyphus function x -> A073053(x) to reach 123.

123, 101, 0, 20, 11, 1

Offset: 0

Author

N. J. A. Sloane, May 12 2019

Keywords

• nonn
• base
• more

Comments

a(n) = index of first n in A073054.

a(6) is currently unknown.

Examples

			0 -> 101 -> 123 reaches 123 in two steps, so a(2) = 0.
1 -> 11 -> 22 -> 202 -> 303 -> 123 reaches 123 in 5 steps, so a(5) = 1.
		

References

• M. E. Coppenbarger, Iterations of a modified Sisyphus function, Fib. Q., 56 (No. 2, 2018), 130-141.

Crossrefs

Cf. A073053, A073054, A100961, A171797.

Programs

Mathematica

id[n_]:=IntegerDigits[n]; il[n_]:=If[n!=0,IntegerLength[n],1]
den[n_]:=FromDigits[{Length[Select[id[n],EvenQ]],Length[Select[id[n],OddQ]],il[n]}]; numD[n_]:=Length[FixedPointList[den,n]]-2;
a308004[n_]:=Module[{k=0},While[numD[k]!=n,k++];k];
a308004/@Range[0,5] (* Ivan N. Ianakiev, May 13 2019 *)