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

1,1

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.

Links

Table of n, a(n) for n=1..36.

Wikipedia, Pythagorean triple

Example

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}.

Prog

(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)

Crossrefs

Cf. A002144, A008846.

Subset of A027862.

Sequence in context: A266486 A142484 A087872 * A098890 A012023 A081442

Adjacent sequences: A308338 A308339 A308340 * A308342 A308343 A308344

Keyword

nonn

Author

Torlach Rush, May 20 2019

Status

approved