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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; for a(2): a=377, b=336, c=505; a(3): 6083, 156, 6085; a(4): 693, 1924, 2045;
a(5): 2688, 3016, 4040; a(6): 408, 20806, 20810; 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, ....
The list seems incomplete: why is 46464 = a*b/2 for (a=264, b=352) with a^2 + b^2 = 440^2 not in the list? I get (6, 46464, 48384, 63336, 65856, 66066, 474474, ...) - M. F. Hasler, Jun 06 2024
LINKS
FORMULA
Intersection of A002113 and A009112. - M. F. Hasler, Jun 06 2024
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 *)
PROG
(PARI) for(n=1, oo, is_A009112(a=A002113(n)) && print1(a", ")) \\ or better:
A101450_row(n) = select(is_A009112, A002113_row(n)) \\ row n = the n-digit terms - M. F. Hasler, Jun 06 2024
CROSSREFS
Cf. A101439.
Sequence in context: A323725 A259162 A076913 * A101439 A099112 A172750
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 June 23 17:30 EDT 2024. Contains 373653 sequences. (Running on oeis4.)