A340300 - OEIS

A340300

a(n) is the number of iterations for n to reach 1 under the following scheme. If k == 0 (mod 3), then k -> k/3, if k == 1 (mod 3) k -> 2k, and if k == 2 (mod 3) add the middle two divisors of k and divide the result by 3.

0, 1, 1, 3, 2, 2, 3, 2, 2, 3, 4, 4, 4, 2, 3, 5, 3, 3, 5, 2, 4, 4, 3, 3, 4, 3, 3, 4, 4, 4, 6, 4, 5, 5, 4, 5, 6, 4, 5, 4, 3, 3, 5, 3, 4, 4, 6, 6, 5, 3, 4, 5, 4, 4, 5, 3, 6, 6, 3, 3, 6, 5, 5, 4, 3, 5, 5, 4, 4, 4, 4, 4, 6, 5, 5, 4, 3, 4, 5, 3, 4, 5, 5, 5, 4, 4, 5, 4, 5, 5, 4, 3, 7, 5, 3, 5, 7, 4, 6, 5, 6, 6, 6, 4, 5

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

OFFSET

1,4

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

a(1) = 0 since 1 is already at 1 which requires no iteration of the scheme;

a(2) = 1 since (1 + 2)/3 -> 1;

a(3) = 1 since 3/3 -> 1;

a(4) = 3 since 4 -> 8 -> (2+4)/3 -> 2 -> 1;

a(5) = 2 since 5 -> (1+5)/2 -> 2 -> 1;

a(6) = 2 since 6 -> 2 -> 1.

MATHEMATICA

f[n_] := f[n] = Switch[ Mod[n, 3], 0, n/3, 1, 2 n, 2, lst = Divisors@ n; len = Length@lst; (lst[[len/2]] + lst[[len/2 + 1]])/3]; a[n_] := Length@NestWhileList[f@# &, n, # > 1 &]; a[n_] := Length@ NestWhileList[f@# &, n, # > 1 &] - 1; Array[a, 105]

CROSSREFS

Cf. A338459 (first occurrence of n).

Sequence in context: A052901 A127807 A122028 * A245070 A270226 A305534

Adjacent sequences: A340297 A340298 A340299 * A340301 A340302 A340303

KEYWORD

nonn

AUTHOR

Ali Sada and Robert G. Wilson v, Jan 03 2021

STATUS

approved