A146945 Hypotenuses of primitive Pythagorean triples which are not prime numbers and which are the hypotenuse of a unique triangle.

25, 125, 169, 289, 625, 841, 1369, 1681, 2197, 2809, 3125, 3721, 4913, 5329, 7921, 9409, 10201, 11881, 12769, 15625, 18769, 22201, 24389, 24649, 28561, 29929, 32761, 37249, 38809, 50653, 52441, 54289, 58081, 66049, 68921, 72361, 76729, 78125

Offset: 1

Author

John Harrison (harrison_uk_2000(AT)yahoo.co.uk), Apr 20 2009

Keywords

• nonn

Comments

Each term is a prime power of the form p^e where p is in A002144 and e>1.

A proper subset of A120960 by eliminating A002144.

A proper subset of A120961 by eliminating A024409.

A proper subset of A008846 by eliminating A002144 and A024409.

A proper subset of A020882 by eliminating A002144, A024409 and duplicate entries.

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A020882, A008846, A002144, A024409, A120960, A120961.

Programs

Mathematica

lst1 = {1, 1}; lst2 = {}; Do[ If[ GCD[m, n] == 1, a = 2m*n; b = m^2 - n^2; c = m^2 + n^2; If[ !PrimeQ@c, AppendTo[lst1, c]]], {m, 3, 1000}, {n, If[OddQ@m, 2, 1], m - 1, 2}]; lst1 = Sort@ lst1; Do[ If[ lst1[[n - 1]] != lst1[[n]] && lst1[[n]] != lst1[[n + 1]], AppendTo[lst2, lst1[[n]]]], {n, 2, Length@ lst1 - 1}]; Take[lst2, 50] (* Robert G. Wilson v, May 02 2009 *)

Extensions

a(7) corrected by and a(17) and further terms from Robert G. Wilson v, May 02 2009

Minor edits to comments. - Ray Chandler, Nov 27 2019