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A101439 Areas of primitive Pythagorean triangles which are palindromes. 1
6, 63336, 474474, 666666, 4383834, 43177134, 460962269064, 60471399317406, 60490233209406, 643869171968346, 6708875775788076, 44703479297430744, 608857707707758806, 44523865177156832544, 683665820959028566386 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Other parts of the n-th triangle are {m,n},{a,b,c}:

a(1): {1,2},{3,4,5};

a(2): {8,21},{377,336,505};

a(3): {1,78},{6083,156,6085};

a(4): {26,37},{693,1924,2045};

a(5): {49,62},{1443,6076,6245};

a(6): {11,158},{24843,3476,25085};

a(7): {2376,2393},{81073,11371536,11371825};

a(8): {4569,4858},{2724403,44392404,44475925};

a(9): {2974,3773},{5390853,22441804,23080205};

a(10): {5402,6829},{17453637,73780516,75816845};

a(11): {121,38132},{1454034783,9227944,1454064065};

a(12): {28407,29336},{53643247,1666695504,1667558545};

a(13): {16593,35986},{1019664547,1194231396,1570319845};

a(14): {3168,241339},{58234476697,1529123904,58254549145};

a(15): {160034,213573},{20002545173,68357882964,71224307485}.

LINKS

Table of n, a(n) for n=1..15.

EXAMPLE

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.

MATHEMATICA

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 (* Robert G. Wilson v, Jan 25 2005 *)

CROSSREFS

Cf. A101450.

Sequence in context: A259162 A076913 A101450 * A099112 A172750 A086897

Adjacent sequences:  A101436 A101437 A101438 * A101440 A101441 A101442

KEYWORD

nonn,base

AUTHOR

Zak Seidov, Jan 18 2005

EXTENSIONS

a(8) & a(10) - a(13) from Robert G. Wilson v, Jan 25 2005

a(14) and a(15) from Ray Chandler, Feb 10 2013

STATUS

approved

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Last modified July 29 10:40 EDT 2021. Contains 346344 sequences. (Running on oeis4.)