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A155186 Primes in A155171. 1


%S 2,7,29,101,107,197,227,457,647,829,1549,1627,2221,2309,2347,2521,

%T 2677,2801,3181,3299,3529,3541,3557,3739,3769,4231,4549,4871,4987,

%U 5651,5827,5881,6037,6079,6637,6827,7517,7639,7937,9787,11621,12041,12329,13009

%N Primes in A155171.

%C Numbers p (prime numbers only) 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.

%t 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;If[PrimeQ[s-1]&&PrimeQ[s+1],If[PrimeQ[p],AppendTo[lst,p]]],{n,8!}];lst

%Y Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178, A155180, A088483, A001844, A096891, A066885, A099776, A110494, A081589, A155185, A019389, A062090, A050150

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jan 21 2009

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Last modified September 19 23:31 EDT 2019. Contains 327207 sequences. (Running on oeis4.)