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A163634 a(n) = (p*(p+4)+1)/2 where (p,p+4) are the n-th cousin prime pair.

%I A163634 #17 Sep 08 2022 08:45:46
%S A163634 11,39,111,219,759,1011,2379,3279,4899,5511,6159,8319,13611,19011,
%T A163634 25311,26679,38919,47739,49611,61599,72579,79599,97239,105339,108111,
%U A163634 119559,125499,189111,208011,227811,274539,288039,297219,340311,365511,370659
%N A163634 a(n) = (p*(p+4)+1)/2 where (p,p+4) are the n-th cousin prime pair.
%H A163634 Vincenzo Librandi, <a href="/A163634/b163634.txt">Table of n, a(n) for n = 1..112</a>
%F A163634 a(n) = (A143206(n) + 1)/2.
%e A163634 a(1) =  (3* 7 + 1)/2 =  11;
%e A163634 a(2) =  (7*11 + 1)/2 =  39;
%e A163634 a(3) = (13*17 + 1)/2 = 111.
%t A163634 (fQ[n_]:=Block[{fi=FactorInteger@n}, Last@#&/@fi=={1, 1}&&Differences[First@#&/@fi]=={4}]; Select[Range@8000000, fQ] + 1)/2 (* _Vincenzo Librandi_ Jan 02 2018 *)
%t A163634 Join[{11},(1+Times@@#)/2&/@Select[Partition[Prime[Range[250]],2,1],#[[2]]- #[[1]]==4&]] (* _Harvey P. Dale_, Apr 04 2022 *)
%o A163634 (Magma) [(p*(p+4)+1)/2: p in PrimesUpTo(1000)| IsPrime(p+4)]; // _Vincenzo Librandi_, May 17 2014
%Y A163634 Cf. A023200, A046132.
%K A163634 nonn
%O A163634 1,1
%A A163634 _Vincenzo Librandi_, Aug 02 2009
%E A163634 Entries checked by _R. J. Mathar_, Aug 07 2009