A155175 Hypotenuse C of primitive Pythagorean triangles such that perimeters are Averages 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.

5, 13, 113, 221, 841, 1741, 3961, 5101, 8581, 9941, 11705, 12013, 20605, 21841, 23113, 26681, 47741, 61601, 78013, 82013, 102605, 103513, 122513, 151801, 276025, 289561, 340313, 418613, 481181, 501001, 660101, 711625, 838513, 901825, 931613

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..35.

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, c]], {n, 8!}]; lst

Crossrefs

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

Sequence in context: A180362 A117527 A228280 * A155185 A213129 A004063

Adjacent sequences: A155172 A155173 A155174 * A155176 A155177 A155178

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

Status

approved