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A068812
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Numbers n such that n and its 10's complement are both triangular numbers; that is, n and 10^k - n (where k is the number of digits in n) are triangular numbers.
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1
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45, 55, 990, 1485, 4005, 4950, 5050, 5995, 8515, 9180, 285390, 499500, 500500, 714610, 1719585, 3064050, 6935950, 8280415, 49000050, 49995000, 50005000, 50999950, 1449668935, 4999950000, 5000050000, 8550331065, 122307408405, 122963116095
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OFFSET
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1,1
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COMMENTS
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Includes 5*10^(2*k+1)-5*10^k and 5*10^(2*k+1)+5*10^k for all k. - Robert Israel, Aug 14 2018
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LINKS
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EXAMPLE
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1485 and 10000 - 1485 = 8515 both are triangular numbers.
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MAPLE
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f:= d -> op(sort(convert(select(t -> (t >= 10^(d-1) and t < 10^d), map(t -> (t^2-1)/8, select(t -> t > 0, map(t -> subs(t, x),
{isolve(x^2+y^2=8*10^d+2)})))), list))):
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MATHEMATICA
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Select[Accumulate[Range[50000]], IntegerQ[Sqrt[8*(10^(IntegerLength[#]) - #) + 1]] &] (* Jayanta Basu, Aug 05 2013 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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