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%I #7 Sep 23 2023 16:20:15
%S 11,101,179,347,569,1049,1229,1301,1487,1667,3557,4127,6089,6761,8627,
%T 9041,10067,11939,12251,14321,19421,25847,28571,29207,30011,30869,
%U 31541,33329,33587,36791,38459,39509,39839,40427,43049,49529,50591,50969
%N The lesser of twin primes p such that p*q+a+b+c are also the lesser of twin primes, (p and q are twin primes, p+2=q, a=p-1,b=(p+q)/2,c=q+1).
%H Harvey P. Dale, <a href="/A168536/b168536.txt">Table of n, a(n) for n = 1..1000</a>
%t lst={};Do[p=Prime[n];q=p+2;If[PrimeQ[q],a=p-1;b=p+1;c=q+1;If[PrimeQ[p*q+a+b+c]&&PrimeQ[p*q+a+b+c+2],AppendTo[lst,p]]],{n,8!}];lst
%t Select[Partition[Prime[Range[5300]],2,1],#[[2]]-#[[1]]==2&&AllTrue[#[[1]]^2+5#[[1]]+{3,5},PrimeQ]&][[;;,1]] (* _Harvey P. Dale_, Sep 23 2023 *)
%Y Cf. A001359, A126334, A128550, A128551
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Nov 28 2009
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