A068812 - OEIS

A068812

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.

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

1,1

COMMENTS

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

LINKS

Robert Israel, Table of n, a(n) for n = 1..1890

EXAMPLE

1485 and 10000 - 1485 = 8515 both are triangular numbers.

MAPLE

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))):

seq(f(d), d=1..20); # Robert Israel, Aug 14 2018

MATHEMATICA

Select[Accumulate[Range[50000]], IntegerQ[Sqrt[8*(10^(IntegerLength[#]) - #) + 1]] &] (* Jayanta Basu, Aug 05 2013 *)

CROSSREFS

Sequence in context: A168108 A037042 A119208 * A119071 A119158 A119204

Adjacent sequences: A068809 A068810 A068811 * A068813 A068814 A068815

KEYWORD

nonn,base,look

AUTHOR

Amarnath Murthy, Mar 07 2002

EXTENSIONS

More terms from Sascha Kurz, Mar 17 2002

Seven additional terms from Jayanta Basu, Aug 05 2013

STATUS

approved