A308341 Hypotenuses of primitive Pythagorean triangles two sides of which are Pythagorean primes.

13, 421, 1861, 5101, 16381, 60901, 83641, 100801, 106261, 135721, 161881, 205441, 218461, 337021, 388081, 431521, 571381, 637321, 697381, 926161, 1108561, 1460341, 1515541, 1806901, 1899301, 2334961, 2574181, 2601481, 2740141, 2834581, 2853661, 3248701, 3403441, 3723721, 3889261, 4503001

Offset: 1

Author

Torlach Rush, May 20 2019

Keywords

• nonn

Comments

Hypotenuses of primitive Pythagorean triangles of the form (2m+1, 2m^2+2m, 2m^2+2m+1), where the hypotenuse and longer leg differ by one.

Except for the first term a(n) is of the form 60k + 1, hence the longer leg is 60k. 60 is the largest number that always divides the product of the sides of any Pythagorean triangle.

Examples

			13 is a term because 13 and 5 are Pythagorean primes and are sides of {5,12,13}.
421 is a term because 421 and 29 are Pythagorean primes and are sides of {29,420,421}.
1861 is a term because 1861 and 61 are Pythagorean primes and are sides of {61,1860,1861}.
5101 is a term because 5101 and 101 are Pythagorean primes and are sides of {101,5100,5101}.
		

Links

• Wikipedia, Pythagorean triple

Crossrefs

Cf. A002144, A008846.

Subset of A027862.

Programs

PARI

hyp(n) = {return((2*((n-1)/2)^2) + (2*((n-1)/2)) + 1);}
lista(n) = forprime(p=2, n, if((p%4 == 1) && isprime(p) && isprime(hyp(p)), print1(hyp(p), ", ")));
lista(3100)