A308004 - OEIS

%I #15 May 13 2019 19:12:22

%S 123,101,0,20,11,1

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

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

%C a(6) is currently unknown.

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

%e 0 -> 101 -> 123 reaches 123 in two steps, so a(2) = 0.

%e 1 -> 11 -> 22 -> 202 -> 303 -> 123 reaches 123 in 5 steps, so a(5) = 1.

%t id[n_]:=IntegerDigits[n]; il[n_]:=If[n!=0,IntegerLength[n],1]

%t den[n_]:=FromDigits[{Length[Select[id[n],EvenQ]],Length[Select[id[n],OddQ]],il[n]}]; numD[n_]:=Length[FixedPointList[den,n]]-2;

%t a308004[n_]:=Module[{k=0},While[numD[k]!=n,k++];k];

%t a308004/@Range[0,5] (* _Ivan N. Ianakiev_, May 13 2019 *)

%Y Cf. A073053, A073054, A100961, A171797.

%K nonn,base,more

%O 0,1

%A _N. J. A. Sloane_, May 12 2019