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A362310 Irregular triangle read by rows (row length A056220). Row n lists the integer solutions for x in the equation x - 10^n = x/y (x and y are integers).

%I A362310 #32 May 21 2023 09:47:06
%S A362310 2,5,8,9,11,12,15,20,50,75,80,90,95,96,98,99,101,102,104,105,110,120,
%T A362310 125,150,200,500,750,800,875,900,950,960,975,980,990,992,995,996,998,
%U A362310 999,1001,1002,1004,1005,1008,1010,1020,1025,1040,1050,1100,1125,1200,1250,1500,2000
%N A362310 Irregular triangle read by rows (row length A056220). Row n lists the integer solutions for x in the equation x - 10^n = x/y (x and y are integers).
%F A362310 Sum of row n = 2*(n+1)^2*10^n.
%F A362310 T(n, k) = 10^n - A056538(10^n, k+2), k < (n+1)^2-1.
%F A362310 T(n, k) = 10^n + A027750(10^n, k+2 - (n+1)^2), (n+1)^2-2 < k < 2*(n+1)^2-1.
%e A362310 Triangle begins:
%e A362310   2
%e A362310   5, 8, 9, 11, 12, 15, 20
%e A362310   50, 75, 80, 90, 95, 96, 98, 99, 101, 102, 104, 105, 110, 120, 125, 150, 200
%e A362310   ...
%e A362310 Corresponding values for y in the equation:
%e A362310    2
%e A362310   -1,-4,-9, 11, 6, 3, 2
%e A362310   -1,-3,-4,-9,-19,-24,-49,-99, 101, 51, 26, 21, 11, 6, 5, 3, 2
%o A362310 (PARI) row(n) = {my(d = divisors(10^n));my(v = concat(vector((n+1)^2,t,10^n)-Vecrev(d),vector((n+1)^2,t,10^n)+d));v[^1]};
%o A362310 (MATLAB)
%o A362310 function a = A362310( max_row )
%o A362310     r = 2; a= [];
%o A362310     for n = 1:max_row
%o A362310         d = divisors(10^(n-1));
%o A362310         a = [a 10^(n-1)-d(end-1:-1:1) 10^(n-1)+d];
%o A362310     end
%o A362310 end
%Y A362310 Cf. A027750, A056220, A056538, A362311.
%K A362310 nonn,tabf,easy
%O A362310 0,1
%A A362310 _Thomas Scheuerle_, Apr 15 2023