A364801 -id:A364801 - cp's OEIS frontend

A364800 The number of iterations that n requires to reach 1 under the map x -> A356874(x).

0, 1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

Amiram Eldar, Aug 08 2023

a(n) is well-defined since A356874(1) = 1, and A356874(n) < n for n >= 2.

			For n = 3 the trajectory is 3 -> 2 -> 1. The number of iterations is 2, thus a(3) = 2.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A356874.

Similar sequences: A003434, A364801.

f[n_] := f[n] = Module[{d = IntegerDigits[n, 2], nd}, nd = Length[d]; Total[d * Fibonacci[Range[nd, 1, -1]]]]; (* A356874 *)
a[n_] := Length@ NestWhileList[f, n, # > 1 &] - 1; Array[a, 100]

f(n) = {my(b = binary(n), nb = #b); sum(i = 1, nb, b[i] * fibonacci(nb - i + 1));} \\ A356874
a(n) = if(n == 1, 0, a(f(n)) + 1);

a(n) = a(A356874(n)) + 1, for n >= 2.

A364803 Smallest number that reaches a fixed point after n iterations of the map x -> A022290(x).

Original entry on oeis.org

0, 4, 5, 6, 7, 10, 14, 23, 46, 117, 442, 3006, 47983, 2839934, 918486751, 3769839124330

Offset: 0

Amiram Eldar, Aug 08 2023

a(n) is the smallest number k such that A364801(k) = n.

Cf. A022290, A364801.

Similar sequences: A007755, A364802.

f[n_] := f[n] = Module[{d = IntegerDigits[n, 2], nd}, nd = Length[d]; Total[d * Fibonacci[Range[nd + 1, 2, -1]]]]; (* A022290 *)
iternum[n_] := -2 + Length@ FixedPointList[f, n]; (* A364801 *)
seq[kmax_] := Module[{s = {}, imax = -1, i}, Do[i = iternum[k]; If[i > imax, imax = i; AppendTo[s, k]], {k, 0, kmax}]; s]
seq[10^6]

f(n) = {my(b = binary(n), nb = #b); sum(i = 1, nb, b[i] * fibonacci(nb - i + 2)); } \\ A022290
iternum(n) = if(n < 4, 0, iternum(f(n)) + 1); \\ A364801
lista(kmax) = {my(imax = -1, i1); for(k = 0, kmax, i = iternum(k); if(i > imax, imax = i; print1(k, ", ")));}

a(15) from Martin Ehrenstein, Aug 25 2023

cp's OEIS Frontend

A364800 The number of iterations that n requires to reach 1 under the map x -> A356874(x).

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