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%I #12 Sep 08 2022 08:45:33
%S 3371,4091,5231,18521,42179,45119,48821,49121,71711,72101,75539,83639,
%T 91571,94151,94559,115979,117191,128111,128339,157769,179819,186299,
%U 189491,203321,208889,213359,233159,248201,250049,251969,259451,267299,273899,275159
%N Lesser of twin primes p1 such that p1^3 + p2^2 are average of twin primes. p1 and p2 twin primes, p1 < p2.
%H Amiram Eldar, <a href="/A139778/b139778.txt">Table of n, a(n) for n = 1..10000</a>
%t a={};Do[p1=Prime[n];p2=Prime[n+1];pp=p1^3+p2^2;If[(p2-p1)==2&&PrimeQ[pp-1]&&PrimeQ[pp+1],AppendTo[a,p1]],{n,10^4}];Print[a];
%t atpQ[{p1_,p2_}]:=Module[{c=p1^3+p2^2},And@@PrimeQ[{c-1,c+1}]]; Transpose[ Select[ Select[Partition[Prime[Range[100000]],2,1],Last[#] - First[#] == 2&],atpQ]][[1]] (* _Harvey P. Dale_, Jul 13 2012 *)
%o (Magma) [p: p in PrimesUpTo(280000)| IsPrime(p+2) and IsPrime(a-1) and IsPrime(a+1) where a is p^3+(p+2)^2]; // _Marius A. Burtea_, Dec 31 2019
%Y Cf. A001359, A006512, A001097.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, May 16 2008
%E More terms from _Harvey P. Dale_, Jul 13 2012
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