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

0,1

Comments

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

a(6) is currently unknown.

References

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

Links

Table of n, a(n) for n=0..5.

Example

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.

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 *)

Crossrefs

Cf. A073053, A073054, A100961, A171797.

Sequence in context: A123171 A125097 A302211 * A192231 A341992 A077378

Adjacent sequences: A308001 A308002 A308003 * A308005 A308006 A308007

Keyword

nonn,base,more

Author

N. J. A. Sloane, May 12 2019

Status

approved