1,1

Compare areas of primitive Pythagorean triangles which are palindromes, A101439. Are these lists full? What are the next cases?

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;

a(2): 377, 336, 505; a(3): 6083, 156, 6085; a(4): 693, 1924, 2045; a(5): 2688, 3016, 4040;

a(7): 1443, 6076, 6245; a(8): 8008, 10506, 13210; a(9): 15392, 5544, 16360; a(10): 24843, 3476, 25085;

a(11): 12432, 98176, 98960; a(12): 155448, 82214, 175850; a(13): 23168, 4193376, 4193440;

a(14): 81073, 11371536, 11371825; a(15): 304928, 4292904, 4303720; a(16): 3420732, 2849024, 4451780;

a(17): 2724403, 44392404, 44475925; a(18): 5390853, 22441804, 23080205; a(19): 17453637, 73780516, 75816845;

a(20): 1454034783, 9227944, 1454064065; a(21): 53643247, 1666695504, 1667558545;

a(22): 1019664547, 1194231396, 1570319845; a(23): 1804499368, 5363316426, 5658743770, ....

666666 is a member, as it is a palindromic number and is area of

Pythagorean triangle with legs a=693, b=1924 and hypotenuse c=2045.

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}] (from Robert G. Wilson v Jan 29 2005)

Cf. A101439.

Sequence in context: A013838 A118859 A076913 this_sequence A101439 A099112 A086897

Adjacent sequences: A101447 A101448 A101449 this_sequence A101451 A101452 A101453

base,nonn

Zak Seidov (zakseidov(AT)yahoo.com), Jan 19 2005

a(16), a(17), a(19)-a(23) from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 31 2005