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Triangular numbers representable as x*y+x+y such that x and y are triangular numbers, x>=y>0.
6

%I #7 Aug 11 2015 15:50:34

%S 3,15,21,91,120,153,351,406,703,741,1891,3081,3403,4465,5151,5565,

%T 6555,9453,9591,18721,22791,23871,38226,39903,46056,52326,79401,85491,

%U 91378,104653,159895,187578,207690,222111,227475,229503,266815,274911,280875,326028,334971,354903

%N Triangular numbers representable as x*y+x+y such that x and y are triangular numbers, x>=y>0.

%C A subsequence of A000217.

%C Up to 10^12, only 4 terms admit two representations, namely 3081, 22791, 410871 and 1675365. - _Giovanni Resta_, Jul 19 2015

%H Giovanni Resta, <a href="/A259745/b259745.txt">Table of n, a(n) for n = 1..509</a> (terms < 10^12)

%e a(1) = 3 = 1*1 + 1 + 1.

%e a(2) = 15 = 3*3 + 3 + 3.

%e a(3) = 21 = 10*1 + 10 + 1.

%e a(4) = 91 = 45*1 + 45 + 1.

%e a(5) = 120 = 10*10 + 10 + 10.

%e a(6) = 153 = 6*21 + 6 + 21.

%Y Cf. A000217, A259746.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Jul 04 2015