Pythagorean triple where the hypotenuse and the odd leg are prime.

[Davide Rotondo]

I think I found something interesting...
In a Pythagorean triple, only the hypotenuse and the odd leg can be prime; Triples of this genus with a side less than 1000 are:
(3, 4, 5),
(5, 12, 13),
(11, 60, 61),
(19, 180, 181),
(29, 420, 421),
(59, 1740, 1741),
(61, 1860, 1861),
(71, 2520, 2521),
(79, 3120, 3121),
(101, 5100, 5101),
(131, 8580, 8581),
(139, 9660, 9661),
(181, 16380, 16381),
(199, 19800, 19801),
(271, 36720, 36721),
(349, 60900, 60901),
(379, 71820, 71821),
(409, 83640, 83641),
(449, 100800, 100801),
(461, 106260, 106261),
(521, 135720, 135721),
(569, 161880, 161881),
(571, 163020, 163021),
(631, 199080, 199081),
(641, 205440, 205441),
(661, 218460, 218461),
(739, 273060, 273061),
(751, 282000, 282001),
(821, 337020, 337021),
(881, 388080, 388081),
(929, 431520, 431521),
(991, 491040, 491041).
....
I noticed that if you perform a congruence operation of the type hypotenuse modulo shorter leg, you obtain the sequence 2, 3, 6, 10, 15, 30, 31, 36, 40, 51, 66, 70, 91, 100, 136,... which corresponds in the encyclopedia of integer sequences to the sequence
A178659
The numbers n such that n^2 +- (n-1)^2 are prime.

What do you think?

Davide

[Davide Rotondo]

Sorry i realizze it is trivial

--
You received this message because you are subscribed to the Google Groups "SeqFan" group.
To unsubscribe from this group and stop receiving emails from it, send an email to seqfan+un...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/seqfan/fca01589-da39-4b39-bb2c-bdae4b79c14dn%40googlegroups.com.