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Search: id:A101439
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| A101439 |
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Areas of primitive Pythahorean triangles which are palindromes. |
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+0
2
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| 6, 63336, 474474, 666666, 4383834, 43177134, 460962269064, 60471399317406, 60490233209406, 643869171968346, 6708875775788076, 44703479297430744, 608857707707758806
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Other parts of the n_th triangle are for a(1): a=3, b=4, c=5 & area=6 = a*b/2; a(2): a=377, b=336, c=505; a(3): a=6083, b=156, c=6085;
a(4): a=693, b=1924, c=2045; a(5): a=1443, b=6076, c=6245; a(6): a=24843, b=3476, c=25085; a(7): a=81073, b=11371536, c=11371825;
a(8): a=2724403, b=44392404, c=44475925; a(9): a=5390853, b=22441804, c=23080205; a(10): a=17453637, b=73780516, c=75816845;
a(11): a=1454034783, b=9227944, c=1454064065; a(12): a=53643247, b=1666695504, c=1667558545; a(13): a=1019664547, b=1194231396, c=1570319845.
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EXAMPLE
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666666 is a member as it is a palindromic number and is the area of a primitive Pythagorean triangle with legs a=693 & b=1924 and hypotenuse c=2045.
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MATHEMATICA
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lst = {}; Do[ If[ GCD[m, n] == 1, a = IntegerDigits[m*n^3 - n*m^3]; If[ Reverse[a] == a, lst = Sort[ AppendTo[ lst, a]]; Print[{n^2 - m^2, 2m*n, n^2 + m^2, m*n^3 - n*m^3}]]], {n, 55000}, {m, If[ EvenQ[n], 1, 2], n - 1, 2}]; lst (from Robert G. Wilson v Jan 25 2005)
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CROSSREFS
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Sequence in context: A118859 A076913 A101450 this_sequence A099112 A086897 A034208
Adjacent sequences: A101436 A101437 A101438 this_sequence A101440 A101441 A101442
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KEYWORD
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nonn,base
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Jan 18 2005
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EXTENSIONS
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a(8) & a(10) - a(13) from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 25 2005
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