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A374451
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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.
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1
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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
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OFFSET
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2,1
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LINKS
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FORMULA
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T(n, n-1) = 2.
T(2^n, k) = 2.
T(p, k) = A020639(k) for any prime number p and k > 1.
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EXAMPLE
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Triangle T(n, k) begins:
n n-th row
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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
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PROG
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(PARI) T(n, k) = { forprime (p = 2, oo, my (d = valuation(n, p) - valuation(k, p)); if (d, return (p); ); ); }
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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