A364800 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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

MATHEMATICA

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]

PROG

(PARI) 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);

CROSSREFS

Cf. A356874.

Similar sequences: A003434, A364801.

Sequence in context: A084556 A084506 A071578 * A157791 A236857 A156874

Adjacent sequences: A364797 A364798 A364799 * A364801 A364802 A364803

KEYWORD

nonn,base,easy

AUTHOR

Amiram Eldar, Aug 08 2023

STATUS

approved