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A075369 Square associated with twin primes (p,p+2): p(p+2) + 1. Square of the average of twin primes.

%I A075369 #32 Sep 08 2022 08:45:07
%S A075369 16,36,144,324,900,1764,3600,5184,10404,11664,19044,22500,32400,36864,
%T A075369 39204,51984,57600,72900,79524,97344,121104,176400,186624,213444,
%U A075369 272484,324900,360000,381924,412164,435600,656100,675684,685584,736164
%N A075369 Square associated with twin primes (p,p+2): p(p+2) + 1. Square of the average of twin primes.
%H A075369 Reinhard Zumkeller, <a href="/A075369/b075369.txt">Table of n, a(n) for n = 1..10000</a>
%F A075369 a(n) = A037074(n) + 1. - _Jon E. Schoenfield_, Jan 13 2015
%F A075369 a(n) = A014574(n)^2. - _Jon E. Schoenfield_, Jan 14 2015
%F A075369 a(n) = A120875(n) + 2. - _Jason Kimberley_, Oct 22 2015
%p A075369 P:= select(isprime,{seq(2*i+1,i=1..1000)}):
%p A075369 T:= P intersect map(`+`,P,2):
%p A075369 sort(convert(map(t -> (t-1)^2, T), list)); # _Robert Israel_, Nov 18 2015
%t A075369 f[n_]:=Prime[n]*Prime[n+1]+1; lst={}; Do[If[IntegerQ[Sqrt[f[n]]],AppendTo[lst,f[n]]],{n,4*5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 10 2010 *)
%o A075369 (Haskell)
%o A075369 a075369 = (^ 2) . a014574  -- _Reinhard Zumkeller_, Feb 10 2015
%o A075369 (PARI) p=2; forprime(b=3, 1e3, if(b-p==2, print1(b*p+1", ")); p=b) \\ _Altug Alkan_, Nov 10 2015
%o A075369 (Magma) [a: n in [1..300] | IsSquare(a) where a is NthPrime(n)*NthPrime(n+1)+1]; // _Vincenzo Librandi_, Nov 19 2015
%Y A075369 Cf. A014574, A037074, A120875.
%K A075369 nonn
%O A075369 1,1
%A A075369 _Amarnath Murthy_, Sep 20 2002