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
Keywords
Examples
see A165250.
Programs
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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