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
Examples
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.
Programs
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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 *) -
PARI
for(n=2,oo, is_A024365(a=A002113(n)) && print1(a", ")) \\ Could be made to a function returning, e.g., the n-th row := the n-digit terms. - M. F. Hasler, Jun 06 2024
Formula
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
Comments