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A345417 Table read by upward antidiagonals: Given m, n >= 1, write gcd(prime(m),prime(n)) as d = u*prime(m)+v*prime(n) where u, v are minimal; T(m,n) = u.

%I A345417 #16 Jun 25 2021 00:34:10
%S A345417 0,1,-1,1,0,-2,1,-1,2,-3,1,1,0,-2,-5,1,-1,-2,3,4,-6,1,1,1,0,-2,-4,-8,
%T A345417 1,-1,2,2,-3,-5,6,-9,1,1,-2,-1,0,2,7,-6,-11,1,-1,-1,-2,-5,6,5,4,8,-14,
%U A345417 1,-1,2,3,2,0,-3,-8,-9,10,-15,1,1,-1,-3,-4,-3,4,7,10,6,-10,-18
%N A345417 Table read by upward antidiagonals: Given m, n >= 1, write gcd(prime(m),prime(n)) as d = u*prime(m)+v*prime(n) where u, v are minimal; T(m,n) = u.
%C A345417 The gcd is 1 unless m=n when it is m; v is given in A345418. Minimal means minimize u^2+v^2. We follow Maple, PARI, etc., in setting u=0 and v=1 when m=n. If we ignore the diagonal, the v table is the transpose of the u table.
%e A345417 The u table (this entry) begins:
%e A345417 [0, -1, -2, -3, -5, -6, -8, -9, -11, -14, -15, -18, -20, -21, -23, -26]
%e A345417 [1, 0, 2, -2, 4, -4, 6, -6, 8, 10, -10, -12, 14, -14, 16, 18]
%e A345417 [1, -1, 0, 3, -2, -5, 7, 4, -9, 6, -6, 15, -8, -17, 19, -21]
%e A345417 [1, 1, -2, 0, -3, 2, 5, -8, 10, -4, 9, 16, 6, -6, -20, -15]
%e A345417 [1, -1, 1, 2, 0, 6, -3, 7, -2, 8, -14, -10, 15, 4, -17, -24]
%e A345417 [1, 1, 2, -1, -5, 0, 4, 3, -7, 9, 12, -17, 19, 10, -18, -4]
%e A345417 [1, -1, -2, -2, 2, -3, 0, 9, -4, 12, 11, -13, -12, -5, -11, 25]
%e A345417 [1, 1, -1, 3, -4, -2, -8, 0, -6, -3, -13, 2, 13, -9, 5, 14]
%e A345417 [1, -1, 2, -3, 1, 4, 3, 5, 0, -5, -4, -8, -16, 15, -2, -23]
%e A345417 [1, -1, -1, 1, -3, -4, -7, 2, 4, 0, 15, -14, 17, 3, 13, 11]
%e A345417 [1, 1, 1, -2, 5, -5, -6, 8, 3, -14, 0, 6, 4, -18, -3, 12]
%e A345417 [1, 1, -2, -3, 3, 6, 6, -1, 5, 11, -5, 0, 10, 7, 14, -10]
%e A345417 ...
%e A345417 The v table (A345418) begins:
%e A345417 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
%e A345417 [-1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1]
%e A345417 [-2, 2, 1, -2, 1, 2, -2, -1, 2, -1, 1, -2, 1, 2, -2, 2]
%e A345417 [-3, -2, 3, 1, 2, -1, -2, 3, -3, 1, -2, -3, -1, 1, 3, 2]
%e A345417 [-5, 4, -2, -3, 1, -5, 2, -4, 1, -3, 5, 3, -4, -1, 4, 5]
%e A345417 [-6, -4, -5, 2, 6, 1, -3, -2, 4, -4, -5, 6, -6, -3, 5, 1]
%e A345417 [-8, 6, 7, 5, -3, 4, 1, -8, 3, -7, -6, 6, 5, 2, 4, -8]
%e A345417 [-9, -6, 4, -8, 7, 3, 9, 1, 5, 2, 8, -1, -6, 4, -2, -5]
%e A345417 [-11, 8, -9, 10, -2, -7, -4, -6, 1, 4, 3, 5, 9, -8, 1, 10]
%e A345417 [-14, 10, 6, -4, 8, 9, 12, -3, -5, 1, -14, 11, -12, -2, -8, -6]
%e A345417 [-15, -10, -6, 9, -14, 12, 11, -13, -4, 15, 1, -5, -3, 13, 2, -7]
%e A345417 [-18, -12, 15, 16, -10, -17, -13, 2, -8, -14, 6, 1, -9, -6, -11, 7]
%e A345417 ...
%Y A345417 Cf. A003989, A050873, A345415, A345416, A345418, A345419-A345422.
%K A345417 sign,tabl
%O A345417 1,6
%A A345417 _N. J. A. Sloane_, Jun 19 2021