This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A307894 #29 Jun 22 2022 20:17:33
%S A307894 13,17,37,53,73,97,109,113,137,149,193,197,233,277,317,337,401,449,
%T A307894 457,541,613,641,653,673,709,757,809,821,877,1009,1061,1093,1117,1129,
%U A307894 1201,1289,1297,1381,1481,1549,1733,1873,1877,1913,1933,1997,2017,2053,2153,2213,2221,2377,2417,2437,2557,2797
%N A307894 Hypotenuses of primitive Pythagorean triangles with prime length, having the property that the sum and absolute difference of the shorter legs are both prime numbers.
%C A307894 Replacing the shorter legs with the sum and absolute difference of the shorter legs may result in an integer-sided triangle, but this is not always the case. For example, {5,12,13}->{7,13,17} and {7,13,17} are the sides of a triangle. However, {60,91,109}->{31,109,151}, but {31,109,151} are not the sides of a triangle. If the replacement results in such a triangle, then the triangle is a scalene integer triangle (A070112) with sides of prime length, and a(n) is a term of A070081.
%C A307894 Sequence provides x-value of solutions to the equation 2*x^2 = y^2 + z^2, with x, y and z primes. - _Lamine Ngom_, Apr 30 2022
%e A307894 13 is a term because 12 + 5 = 17 and 12 - 5 = 7.
%e A307894 17 is a term because 15 + 8 = 23 and 15 - 8 = 7.
%e A307894 37 is a term because 35 + 12 = 47 and 35 - 12 = 23.
%Y A307894 Cf. A070081, A070112.
%Y A307894 Subset of A008846.
%Y A307894 Subset of A307880.
%K A307894 nonn
%O A307894 1,1
%A A307894 _Torlach Rush_, May 03 2019