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A308341
Hypotenuses of primitive Pythagorean triangles two sides of which are Pythagorean primes.
0
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.
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
Subset of A027862.
Sequence in context: A266486 A142484 A087872 * A098890 A012023 A081442
KEYWORD
nonn
AUTHOR
Torlach Rush, May 20 2019
STATUS
approved