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%I #10 Aug 25 2023 12:44:53
%S 0,4,5,6,7,10,14,23,46,117,442,3006,47983,2839934,918486751,
%T 3769839124330
%N Smallest number that reaches a fixed point after n iterations of the map x -> A022290(x).
%C a(n) is the smallest number k such that A364801(k) = n.
%t f[n_] := f[n] = Module[{d = IntegerDigits[n, 2], nd}, nd = Length[d]; Total[d * Fibonacci[Range[nd + 1, 2, -1]]]]; (* A022290 *)
%t iternum[n_] := -2 + Length@ FixedPointList[f, n]; (* A364801 *)
%t seq[kmax_] := Module[{s = {}, imax = -1, i}, Do[i = iternum[k]; If[i > imax, imax = i; AppendTo[s, k]], {k, 0, kmax}]; s]
%t seq[10^6]
%o (PARI) f(n) = {my(b = binary(n), nb = #b); sum(i = 1, nb, b[i] * fibonacci(nb - i + 2)); } \\ A022290
%o iternum(n) = if(n < 4, 0, iternum(f(n)) + 1); \\ A364801
%o lista(kmax) = {my(imax = -1, i1); for(k = 0, kmax, i = iternum(k); if(i > imax, imax = i; print1(k, ", ")));}
%Y Cf. A022290, A364801.
%Y Similar sequences: A007755, A364802.
%K nonn,base,more
%O 0,2
%A _Amiram Eldar_, Aug 08 2023
%E a(15) from _Martin Ehrenstein_, Aug 25 2023
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