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A101450 Areas of (not necessarily primitive) Pythagorean triangles which are palindromes. 1
6, 63336, 474474, 666666, 4053504, 4244424, 4383834, 42066024, 42666624, 43177134, 610262016, 6390000936, 48576067584, 460962269064, 654513315456, 4872873782784, 60471399317406, 60490233209406, 643869171968346 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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, ....

LINKS

Table of n, a(n) for n=1..19.

EXAMPLE

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.

MATHEMATICA

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 *)

CROSSREFS

Cf. A101439.

Sequence in context: A323725 A259162 A076913 * A101439 A099112 A172750

Adjacent sequences:  A101447 A101448 A101449 * A101451 A101452 A101453

KEYWORD

base,nonn

AUTHOR

Zak Seidov, Jan 19 2005

EXTENSIONS

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

STATUS

approved

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Last modified April 5 13:02 EDT 2020. Contains 333241 sequences. (Running on oeis4.)