A157184 Lesser of two Pythagorean primes for which the Pythagorean triangles have the same area.

29, 109, 193, 541, 673, 709, 3257, 4201, 6217, 8269, 9109, 10957, 12637, 18013, 22717, 23557, 23689, 27329, 33413, 45553, 47737, 48889, 48953, 55001, 55117, 56473, 56737, 59509, 59921, 62297, 65393, 67061, 68909, 75577, 83477, 84221

Offset: 1

Author

David Broadhurst, Feb 26 2009

Keywords

• nonn

Links

• Shiv K. Gupta, Areas of Pythagorean Triangles, post to NMBRTHRY list, Dec 23 2008

Programs

PARI

{Q=Qfb(1,0,1); forprime(p=5,10^5, p%4==1|next; t=qfbsolve(Q,p); A=t[1]*t[2]*(t[1]^2-t[2]^2); fordiv( A,d, if( issquare(d^2+(2*A/d)^2,&q) && isprime(q) && q>p, print1(p", ");break)))}

Formula

A157184 = { A002144(k) | exists m>k : A145010(m)=A145010(k) }