A155173 Short leg A of primitive Pythagorean triangles such that perimeter s is average of twin prime pairs, q=p+1, A=q^2-p^2, C=q^2+p^2, B=2*p*q, s=A+B+C; s -/+ 1 are primes.

3, 5, 15, 21, 41, 59, 89, 101, 131, 141, 153, 155, 203, 209, 215, 231, 309, 351, 395, 405, 453, 455, 495, 551, 743, 761, 825, 915, 981, 1001, 1149, 1193, 1295, 1343, 1365, 1421, 1529, 1659, 1853, 2105, 2171, 2205, 2255, 2373, 2409, 2411, 2451, 2513, 2561, 2649

Offset

1,1

Comments

With p=1, then q=2,a=3,b=4,c=5, and s=12-+1 (11, 13) both primes.

Links

Table of n, a(n) for n=1..50.

Mathematica

lst={}; Do[p=n; q=p+1; a=q^2-p^2; c=q^2+p^2; b=2*p*q; s=a+b+c; If[PrimeQ[s-1]&&PrimeQ[s+1], AppendTo[lst, a]], {n, 8!}]; lst

Crossrefs

Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171.

Sequence in context: A101129 A177916 A128396 * A202505 A210111 A121219

Adjacent sequences: A155170 A155171 A155172 * A155174 A155175 A155176

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

Extensions

Name edited by Zak Seidov, Mar 21 2014

Status

approved