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).

2, 5, 8, 9, 11, 12, 15, 20, 50, 75, 80, 90, 95, 96, 98, 99, 101, 102, 104, 105, 110, 120, 125, 150, 200, 500, 750, 800, 875, 900, 950, 960, 975, 980, 990, 992, 995, 996, 998, 999, 1001, 1002, 1004, 1005, 1008, 1010, 1020, 1025, 1040, 1050, 1100, 1125, 1200, 1250, 1500, 2000

Offset: 0

Author

Thomas Scheuerle, Apr 15 2023

Keywords

• nonn
• tabf
• easy

Examples

			Triangle begins:
  2
  5, 8, 9, 11, 12, 15, 20
  50, 75, 80, 90, 95, 96, 98, 99, 101, 102, 104, 105, 110, 120, 125, 150, 200
  ...
Corresponding values for y in the equation:
   2
  -1,-4,-9, 11, 6, 3, 2
  -1,-3,-4,-9,-19,-24,-49,-99, 101, 51, 26, 21, 11, 6, 5, 3, 2
		

Crossrefs

Cf. A027750, A056220, A056538, A362311.

Programs

MATLAB

function a = A362310( max_row )
    r = 2; a= [];
    for n = 1:max_row
        d = divisors(10^(n-1));
        a = [a 10^(n-1)-d(end-1:-1:1) 10^(n-1)+d];
    end
end

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]};

Formula

Sum of row n = 2*(n+1)^2*10^n.

T(n, k) = 10^n - A056538(10^n, k+2), k < (n+1)^2-1.

T(n, k) = 10^n + A027750(10^n, k+2 - (n+1)^2), (n+1)^2-2 < k < 2*(n+1)^2-1.