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

0,1

Links

Table of n, a(n) for n=0..55.

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.

Example

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

Prog

(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]};
(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

Crossrefs

Cf. A027750, A056220, A056538, A362311.

Sequence in context: A231756 A212591 A153275 * A161154 A174438 A176061

Adjacent sequences: A362307 A362308 A362309 * A362311 A362312 A362313

Keyword

nonn,tabf,easy

Author

Thomas Scheuerle, Apr 15 2023

Status

approved