A155178 Numbers p of primitive Pythagorean triangles such that perimeters and products of 3 sides are Averages of twin prime pairs, q=p+1, a=q^2-p^2, c=q^2+p^2, b=2*p*q, ar=a*b/2; s=a+b+c, s-+1 are primes, pr=a*b*c, pr-+1 are primes.

1, 7916, 35882, 37816, 47491, 128429, 131830, 146471, 154799, 157579, 170219, 174964, 187544, 207829, 208039, 222887, 223142, 262502, 291544, 319825, 327602, 331627, 353857, 476681, 477659, 494207, 522025, 537454, 540682, 558161, 571670

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

Keywords

• nonn

Comments

p=1,q=2,a=3,b=4,c=5,s=12-+1 primes,pr=3*4*5=60-+1 primes, ...

Crossrefs

Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177

Programs

Mathematica

lst={};Do[p=n;q=p+1;a=q^2-p^2;c=q^2+p^2;b=2*p*q;ar=a*b/2;s=a+b+c;pr=a*b*c;If[PrimeQ[s-1]&&PrimeQ[s+1]&&PrimeQ[pr-1]&&PrimeQ[pr+1],AppendTo[lst,n]],{n,3*9!}];lst