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 A319812 Square array read by antidiagonals: T(n,k) = (1 + i)-adic valuation of n + k*i, n >= 0, k >= 0, or -1 if n + k*i = 0. 0
 -1, 0, 0, 2, 1, 2, 0, 0, 0, 0, 4, 1, 3, 1, 4, 0, 0, 0, 0, 0, 0, 2, 1, 2, 1, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 6, 1, 3, 1, 5, 1, 3, 1, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, 3, 1, 4, 1, 3, 1, 4, 1, 3, 1, 4 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Equivalently, T(n,k) = 2-adic valuation of n^2 + k^2. Table is symmetric with respect to the main diagonal. For any Gaussian integer z = x + y*i, its (1 + i)-adic valuation is T(|x|,|y|) if z != 0 and +oo if z = 0. LINKS FORMULA For n + k*i != 0: T(n,k) = v(n^2 + k^2, 2) where v(k, 2) = A007814(k) is the 2-adic valuation of k. T(n,k) = 2*min{v(n, 2), v(k, 2)} if v(n, 2) != v(k, 2), otherwise v(n, 2) + v(k, 2) + 1. Here v(0, 2) = +oo. EXAMPLE Table begins X 0 2 0 4 0 2 0 6 0 2 0 4 0 2 0 8 ... 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 ... 2 0 3 0 2 0 3 0 2 0 3 0 2 0 3 0 2 ... 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 ... 4 0 2 0 5 0 2 0 4 0 2 0 5 0 2 0 4 ... 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 ... 2 0 3 0 2 0 3 0 2 0 3 0 2 0 3 0 2 ... 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 ... 6 0 2 0 4 0 2 0 7 0 2 0 4 0 2 0 6 ... 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 ... 2 0 3 0 2 0 3 0 2 0 3 0 2 0 3 0 2 ... 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 ... 4 0 2 0 5 0 2 0 4 0 2 0 5 0 2 0 4 ... 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 ... 2 0 3 0 2 0 3 0 2 0 3 0 2 0 3 0 2 ... 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 ... 8 0 2 0 4 0 2 0 6 0 2 0 4 0 2 0 9 ... ... (X denotes that (1 + i)-adic valuation of 0 is +oo) PROG (PARI) T(n, k) = valuation(n^2+k^2, 2) CROSSREFS Cf. A007814. Sequence in context: A070965 A079548 A175620 * A079071 A322795 A050602 Adjacent sequences:  A319809 A319810 A319811 * A319813 A319814 A319815 KEYWORD sign,easy,tabl AUTHOR Jianing Song, Sep 28 2018 STATUS approved

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Last modified March 30 22:55 EDT 2020. Contains 333132 sequences. (Running on oeis4.)