

A067755


Even legs of Pythagorean triangles whose other leg and hypotenuse are both prime.


8



4, 12, 60, 180, 420, 1740, 1860, 2520, 3120, 5100, 8580, 9660, 16380, 19800, 36720, 60900, 71820, 83640, 100800, 106260, 135720, 161880, 163020, 199080, 205440, 218460, 273060, 282000, 337020, 388080, 431520, 491040, 531480, 539760, 552300
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OFFSET

1,1


COMMENTS

Apart from the first two terms, every term is divisible by 60 and is of the form 450*k^2 +/ 30*k or 450*k^2 +/ 330*k + 60 for some k.
In such a triangle, this even leg is always the longer leg, and the hypotenuse = a(n) + 1. The Pythagorean triples are (A048161(n), a(n), A067756(n)), so, for a(2) = 12, the corresponding Pythagorean triple is (5, 12, 13).  Bernard Schott, Apr 12 2023


LINKS



FORMULA



EXAMPLE

4 is a term: in the right triangle (3, 4, 5), 3 and 5 are prime.
5100 is a term: in the right triangle (101, 5100, 5101), 101 and 5101 are prime.


MATHEMATICA

lst={}; Do[q=(Prime[n]^2+1)/2; If[PrimeQ[q], AppendTo[lst, (Prime[n]^21)/2]], {n, 200}]; lst (* Frank M Jackson, Nov 02 2013 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



