A101439 Areas of primitive Pythagorean triangles which are palindromes.

6, 63336, 474474, 666666, 4383834, 43177134, 460962269064, 60471399317406, 60490233209406, 643869171968346, 6708875775788076, 44703479297430744, 608857707707758806, 44523865177156832544, 683665820959028566386

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