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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, -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
2,4
COMMENTS
See A374451 for the corresponding prime numbers.
FORMULA
T(n, 1) = A067029(n).
T(n, n-1) = A094267(n-2).
EXAMPLE
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
PROG
(PARI) T(n, k) = { forprime (p = 2, oo, my (d = valuation(n, p) - valuation(k, p)); if (d, return (d); ); ); }
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Rémy Sigrist, Jul 09 2024
STATUS
approved