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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).
2
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
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
KEYWORD
nonn,tabf,easy
AUTHOR
Thomas Scheuerle, Apr 15 2023
STATUS
approved