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

Author

Peter Kagey, Jan 25 2016

Keywords

• tabl
• nonn

Comments

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

Examples

			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
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000
• "ModernModest", Reddit discussion

Crossrefs

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

Programs

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 *)