A374462 Triangle T(n, k), n > 1, k = 1..n-1, read by rows; T(n, k) equals the p-adic valuation of n minus the p-adic valuation of k where p is the least prime number such that this quantity is nonzero.

1, 1, -1, 2, 1, 2, 1, -1, -1, -2, 1, 1, 1, -1, 1, 1, -1, -1, -2, -1, -1, 3, 2, 3, 1, 3, 2, 3, 2, -1, 1, -2, 2, -1, 2, -3, 1, 1, 1, -1, 1, -1, 1, -2, 1, 1, -1, -1, -2, -1, -1, -1, -3, -2, -1, 2, 1, 2, 1, 2, 1, 2, -1, 2, 1, 2, 1, -1, -1, -2, -1, -1, -1, -3, -2, -1, -1, -2

Offset: 2

Author

Rémy Sigrist, Jul 09 2024

Keywords

• sign
• tabl

Comments

See A374451 for the corresponding prime numbers.

Examples

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

Links

• Rémy Sigrist, Scatterplot of (x, y) such that T(x, y) > 0 and x <= 2^9

Crossrefs

Cf. A067029, A094267, A374381, A374451.

Programs

PARI

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

Formula

T(n, 1) = A067029(n).

T(n, n-1) = A094267(n-2).