A307880 Hypotenuses of primitive pythagorean triangles having the property that the sum and absolute difference of the shorter legs are both prime numbers.

13, 17, 25, 37, 53, 65, 73, 85, 97, 109, 113, 137, 149, 193, 197, 205, 221, 233, 277, 289, 305, 317, 337, 365, 401, 425, 445, 449, 457, 485, 505, 533, 541, 613, 625, 641, 653, 673, 697, 709, 725, 757, 785, 793, 809, 821, 877, 905, 925, 949, 1009

Offset: 1

Author

Torlach Rush, May 02 2019

Keywords

• nonn

Examples

			13 is a term because 12 + 5 = 17 and 12 - 5 = 7.
17 is a term because 15 + 8 = 23 and 15 - 8 = 7.
25 is a term because 24 + 7 = 31 and 24 - 7 = 17.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Subset of A008846.

Programs

Mathematica

Sqrt[#[[1]]^2+#[[2]]^2]&/@Select[Union[Sort/@({Times@@#,(Last[#]^2-First[ #]^2)/2}&/@(Select[Subsets[Range[1,51,2],{2}],GCD@@#==1&]))],AllTrue[ {Total[#],#[[2]]-#[[1]]},PrimeQ]&]//Union (* Harvey P. Dale, Sep 25 2022 *)