[ January 23, 2005 ]
List of palindromic areas of primitive Pythagorean triangles
Zakir Seidov (website)

“ I saw before your Palindromic Pythagorean Triples,
and it inspired me to look for palindromic areas.
I've just sent to OEIS the 'all I know' cases of
palindromic areas of primitive Pythagorean triangles.
Hope it'd be interesting to visitors of your great site.”

{area, leg a, leg b, hypo c} {6, 3, 4, 5}, Primitive! {63336, 336, 377, 505}, Primitive! {474474, 156, 6083, 6085},Primitive! {666666, 693, 1924, 2045}, Primitive! {4053504, 2688, 3016, 4040}, {4244424, 408, 20806, 20810}, {4383834, 1443, 6076, 6245}, Primitive! {42066024, 8008, 10506, 13210}, {42666624, 5544, 15392, 16360}, {43177134, 3476, 24843, 25085}, Primitive! {610262016, 12432, 98176, 98960}, {6390000936, 82214, 155448, 175850}, {48576067584, 23168, 4193376, 4193440}, {460962269064, 81073, 11371536, 11371825}, Primitive! {654513315456, 304928, 4292904, 4303720}, {60490233209406, 5390853, 22441804, 23080205}, Primitive!

Note that we now have eight new cases of pal_areas
of primitive Pythagorean triangles (PPTs) !
( primitive means "with no common factors" )

ID Number: A101439 URL: https://oeis.org/A101439 Sequence: 63336,474474,666666,4383834,43177134 Name: Areas of primitive Pythagorean triangles which are palindromes. Comments: Other triangles are: n=1, a=336, b=377, c=505; n=2, a=156, b=6083, c=6085; n=4, a=1443, b=6076, c=6245; n=5, a=3476, b=24843, c=25085. What is the next case? Example: 666666 is a member, as it is a palindromic number, and is area of primitive Pythagorean triangle with legs a=693, b=1924, and hypotenuse c=2045. Keywords: more,nonn,base,new Offset: 1 Author(s): Zak Seidov (seidovzf(AT)yahoo.com), Jan 18 2005 ID Number: A101450 URL: https://oeis.org/A101450 Sequence: 6,63336,474474,666666,4053504,4244424,4383834,42066024, 42666624,43177134,610262016,6390000936,48576067584, 460962269064,654513315456,60490233209406 Name: Areas of (not-necessarily-primitive) Pythagorean triangles which are palindromes. Comments: Compare areas of primitive Pythagorean triangles which are palindromes, A101439. Are these lists full? What are the next cases? 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. See also: Cf. A101439. Keywords: base,more,nonn,new Offset: 0 Author(s): Zak Seidov (seidovzf(AT)yahoo.com), Jan 19 2005

Did you know that 474474 (156^2 + 6083^2 = 6085^2)
is also the product of three consecutive numbers
namely 77 x 78 x 79.

Note that in the 2nd case hypotenuse 505 is also palindromic!

From Mike Keith's webpage The Number of the Beast
There are only two known Pythagorean triangles
whose area is a repdigit number:
(3, 4, 5) with area 6
(693, 1924, 2045) with area 666666
It is not known whether there are any others, though a computer
search has verified that there are none with area less than 10⁴⁰.
[see J. Rec. Math, 26(4), Problem 2097 by Monte Zerger]

666666₁₀ remains palindromic when
converted to hexadecimal base i.e., A2C2A₁₆

On the internet we can consult a general list with 'leg b'
up to 10000 : Pythagorean Triple Table by Michael Somos