A165261 Long legs of primitive Pythagorean triples which have a perimeter which is the average of a twin prime pair.

4, 12, 77, 112, 143, 195, 209, 220, 299, 420, 425, 520, 527, 629, 700, 840, 868, 988, 1023, 1085, 1127, 1209, 1305, 1421, 1480, 1720, 1740, 1900, 2001, 2021, 2255, 2296, 2320, 2331, 2332, 2499, 2520, 2548, 2583, 2604, 2752, 2829, 2964, 3021, 3256, 3311

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Example

see A165250.

Mathematica

amax=10^5; lst={}; k=0; q=12!; Do[If[(e=((n+1)^2-n^2))>amax, Break[]]; Do[If[GCD[m, n]==1, a=m^2-n^2; b=2*m*n; If[GCD[a, b]==1, If[a>b, {a, b}={b, a}]; If[a>amax, Break[]]; c=m^2+n^2; x=a+b+c; If[PrimeQ[x-1]&&PrimeQ[x+1], k++; AppendTo[lst, b]]]], {m, n+1, 12!, 2}], {n, 1, q, 1}]; Union@lst

Crossrefs

Cf. A020883, A014574, A165260, A165262.

Sequence in context: A358660 A301340 A244058 * A027145 A299795 A351736

Adjacent sequences: A165258 A165259 A165260 * A165262 A165263 A165264

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Sep 11 2009

Status

approved