A374369 -id:A374369 - cp's OEIS frontend

A374381 Triangle T(n, k), n > 0, k = 0..n-1, read by rows; T(n, k) = (n mod m) - (k mod m) where m = A007978(n-k).

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

Offset: 1

Rémy Sigrist, Jul 07 2024

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

Rémy Sigrist, Scatterplot of (x, y) such that T(x, y) > 0 and x <= 420

Cf. A007978, A213636, A374369.

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

T(n, 0) = A213636(n).

T(n, n-1) = (-1)^(n-1).

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.

Original entry on oeis.org

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

Rémy Sigrist, Jul 08 2024

			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

Cf. A020639, A374369.

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

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.

cp's OEIS Frontend

A374381 Triangle T(n, k), n > 0, k = 0..n-1, read by rows; T(n, k) = (n mod m) - (k mod m) where m = A007978(n-k).

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