A374369 Triangle T(n, k), n > 0, k = 0..n-1, read by rows; T(n, k) is the least m such that n and k differ modulo m.

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

Offset: 1

Author

Rémy Sigrist, Jul 06 2024

Keywords

• nonn
• easy
• tabl

Examples

			Triangle T(n, k) begins:
  n   n-th row
  --  ----------------------------------
   1  2
   2  3, 2
   3  2, 3, 2
   4  3, 2, 3, 2
   5  2, 3, 2, 3, 2
   6  4, 2, 3, 2, 3, 2
   7  2, 4, 2, 3, 2, 3, 2
   8  3, 2, 4, 2, 3, 2, 3, 2
   9  2, 3, 2, 4, 2, 3, 2, 3, 2
  10  3, 2, 3, 2, 4, 2, 3, 2, 3, 2
  11  2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2
  12  5, 2, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2
		

Crossrefs

Cf. A007978, A374381, A374383.

Programs

Mathematica

T[n_,k_]:=Module[{m=2},While[Mod[n,m]==Mod[k,m], m++]; m]; Table[T[n,k],{n,13},{k,0,n-1}]//Flatten (* Stefano Spezia, Jul 12 2024 *)

PARI

T(n, k) = { for (m = 2, oo, if ((n%m) != (k%m), return (m););); }

Formula

T(n, k) = A007978(n-k).