A168536 - OEIS

A168536

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).

%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