A374451 Triangle T(n, k), n > 1, k = 1..n-1, read by rows; T(n, k) is the least prime number p such that the p-adic valuations of n and k differ.

2, 3, 2, 2, 2, 2, 5, 2, 3, 2, 2, 3, 2, 2, 2, 7, 2, 3, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 5, 2, 2, 2, 3, 2, 2, 2, 11, 2, 3, 2, 5, 2, 7, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 13, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 2, 7, 2, 2, 2, 3, 2, 2, 2, 5, 2, 2, 2

Offset: 2

Author

Rémy Sigrist, Jul 08 2024

Keywords

• nonn
• easy
• tabl

Examples

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

Crossrefs

Cf. A020639, A374369.

Programs

PARI

T(n, k) = { forprime (p = 2, oo, my (d = valuation(n, p) - valuation(k, p)); if (d, return (p););); }

Formula

T(n, 1) = A020639(n).

T(n, n-1) = 2.

T(2^n, k) = 2.

T(p, k) = A020639(k) for any prime number p and k > 1.