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%I #13 Sep 25 2022 16:37:16
%S 13,17,25,37,53,65,73,85,97,109,113,137,149,193,197,205,221,233,277,
%T 289,305,317,337,365,401,425,445,449,457,485,505,533,541,613,625,641,
%U 653,673,697,709,725,757,785,793,809,821,877,905,925,949,1009
%N Hypotenuses of primitive pythagorean triangles having the property that the sum and absolute difference of the shorter legs are both prime numbers.
%H Harvey P. Dale, <a href="/A307880/b307880.txt">Table of n, a(n) for n = 1..1000</a>
%e 13 is a term because 12 + 5 = 17 and 12 - 5 = 7.
%e 17 is a term because 15 + 8 = 23 and 15 - 8 = 7.
%e 25 is a term because 24 + 7 = 31 and 24 - 7 = 17.
%t 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 *)
%Y Subset of A008846.
%K nonn
%O 1,1
%A _Torlach Rush_, May 02 2019