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%I #9 Mar 14 2015 16:48:03
%S 6,63336,474474,666666,4053504,4244424,4383834,42066024,42666624,
%T 43177134,610262016,6390000936,48576067584,460962269064,654513315456,
%U 4872873782784,60471399317406,60490233209406,643869171968346
%N Areas of (not necessarily primitive) Pythagorean triangles which are palindromes.
%C Compare areas of primitive Pythagorean triangles which are palindromes, A101439. Are these lists full? What are the next cases?
%C Other parts of the n-th triangle are for a(1): a=3, b=4, c=5 & area=6 = a*b/2; a(6): 408, 20806, 20810;
%C a(2): 377, 336, 505; a(3): 6083, 156, 6085; a(4): 693, 1924, 2045; a(5): 2688, 3016, 4040;
%C a(7): 1443, 6076, 6245; a(8): 8008, 10506, 13210; a(9): 15392, 5544, 16360; a(10): 24843, 3476, 25085;
%C a(11): 12432, 98176, 98960; a(12): 155448, 82214, 175850; a(13): 23168, 4193376, 4193440;
%C a(14): 81073, 11371536, 11371825; a(15): 304928, 4292904, 4303720; a(16): 3420732, 2849024, 4451780;
%C a(17): 2724403, 44392404, 44475925; a(18): 5390853, 22441804, 23080205; a(19): 17453637, 73780516, 75816845;
%C a(20): 1454034783, 9227944, 1454064065; a(21): 53643247, 1666695504, 1667558545;
%C a(22): 1019664547, 1194231396, 1570319845; a(23): 1804499368, 5363316426, 5658743770, ....
%e 666666 is a member, as it is a palindromic number and is area of
%e Pythagorean triangle with legs a=693, b=1924 and hypotenuse c=2045.
%t lst = {}; Do[ a = IntegerDigits[m*n^3 - n*m^3]; If[ Reverse[a] == a, lst = Sort[ AppendTo[ lst, FromDigits[a]]]; Print[{n^2 - m^2, 2m*n, n^2 + m^2, m*n^3 - n*m^3}]], {n, 50000}, {m, n - 1}] (* _Robert G. Wilson v_, Jan 29 2005 *)
%Y Cf. A101439.
%K base,nonn
%O 1,1
%A _Zak Seidov_, Jan 19 2005
%E a(16), a(17), a(19)-a(23) from _Robert G. Wilson v_, Jan 31 2005
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