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

1,1

Links

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

Example

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.

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 *)

Crossrefs

Subset of A008846.

Sequence in context: A104278 A129070 A335036 * A155923 A248215 A283135

Adjacent sequences: A307877 A307878 A307879 * A307881 A307882 A307883

Keyword

nonn

Author

Torlach Rush, May 02 2019

Status

approved