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[ January 23, 2005 ]
Zakir Seidov's (website) list of palindromic
areas of primitive Pythagorean triangles.

" 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:       http://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:       http://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




A000163 Prime Curios! Prime Puzzle
Wikipedia 163 Le nombre 163














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