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%I #17 Feb 11 2018 12:29:14
%S 6,18,37,44,86,91,116,132,247,278,392,613,637,662,798,847,912,1164,
%T 1235,1362,1430,1638,1735,1991,2056,2090,2167,2364,2537,2736,3139,
%U 3478,3751,3867,4298,4422,4553,5202,6068,6391,6500,7241,7859,7957,8378,9309,9793
%N Side of triangle of larger member of a pair of triangular numbers whose sum and difference are triangular.
%C Side lengths where both triangular numbers are the same (A053141) are not included. - _R. J. Mathar_, Feb 11 2018
%D Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 197, nr. 8.
%H R. J. Mathar, <a href="/A185223/b185223.txt">Table of n, a(n) for n = 1..58</a>
%e a(2) = 18, since the pair of triangular numbers 171 = 18*(18+1)/2 and 105 = 14*(14+1)/2 produce the sum 276 = 23*(23+1)/2 and the difference 66 = 11*(11+1)/2 which are both triangular numbers.
%o (PARI) lista(nn) = {v = vector(nn, n, n*(n+1)/2); for (n=2, nn, for (k=1, n-1, if (ispolygonal(v[n]+v[k], 3) && ispolygonal(v[n]-v[k], 3), print1(n, ", "));););} \\ _Michel Marcus_, Jan 08 2015
%Y Cf. A000217, A185128, A185129, A185233, A185243, A185253, A185257, A185258.
%K nonn
%O 1,1
%A _Martin Renner_, Jan 20 2012
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