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

1,2

Comments

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

Links

Table of n, a(n) for n=1..31.

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

Crossrefs

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

Sequence in context: A237969 A256163 A171111 * A031922 A121236 A233976

Adjacent sequences: A155175 A155176 A155177 * A155179 A155180 A155181

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

Status

approved