A268057 Triangle T(n,k), 1<=k<=n, read by rows: T(n,k) = number of iterations of A048158(n, A048158(n, ... A048158(n, k)...)) to reach 0.

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

Offset

1,5

Comments

Each column is periodic: T(n+A003418(k),k) = T(n,k). - Robert Israel, Feb 02 2016

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

"ModernModest", Reddit discussion

Example

T(5, 3) = 3 because the algorithm requires three steps to reach 0.
  5 % 3 = 2
  5 % 2 = 1
  5 % 1 = 0
Triangle begins:
  1
  1 1
  1 2 1
  1 1 2 1
  1 2 3 2 1
  1 1 1 2 2 1
  1 2 2 3 3 2 1
  1 1 2 1 3 2 2 1
  1 2 1 2 3 2 3 2 1
  1 1 2 2 1 3 3 2 2 1
  1 2 3 4 2 3 5 4 3 2 1
  1 1 1 1 2 1 3 2 2 2 2 1

Maple

T:= proc(n, k) option remember; local m;
     if k = 0 then 0 else 1 + procname(n, n mod k) fi
end proc:
seq(seq(T(n, k), k=1..n), n=1..30); # Robert Israel, Feb 02 2016

Mathematica

T[n_, k_] := T[n, k] = If[k == 0, 0, 1 + T[n, Mod[n, k]]];
Table[Table[T[n, k], {k, 1, n}], {n, 1, 30}] // Flatten (* Jean-François Alcover, Jan 31 2023, after Robert Israel *)

Crossrefs

Cf. A003418, A048158, A107435, A268058, A268059, A268060.

Sequence in context: A335234 A353854 A217467 * A107435 A196056 A161095

Adjacent sequences: A268054 A268055 A268056 * A268058 A268059 A268060

Keyword

tabl,nonn

Author

Peter Kagey, Jan 25 2016

Status

approved