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%I #12 Dec 25 2019 04:49:02
%S 180,1620,8820,35280,87120,151380,302580,380880,691920,737280,808020,
%T 1393920,5020020,5767380,7712820,9604980,10281780,11160180,12450420,
%U 12736080,14723280,15138000,17186580,17860500,18663120,18779220,19129680,21300480
%N Numbers n = 5*k^2 such that n - 1 and n + 1 are (twin) primes (thus k=6*m).
%C Original definition: Averages of twin prime pairs n such that n*5 and n/5 are squares.
%C Obviously, n*5 is a square iff n/5 is a square, say k^2. But n=5k^2 can't be the average of a twin prime pair unless it's a multiple of 6, thus k=6m and n=5*36*m^2. - _M. F. Hasler_, Apr 11 2009
%H Amiram Eldar, <a href="/A154672/b154672.txt">Table of n, a(n) for n = 1..10000</a>
%F A154672 = 5*A000290 intersect A014574 = 180*A000290 intersect A014574. - M. F. Hasler, Apr 11 2009
%t lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n*5)^(1/2);If[Floor[s]==s,AppendTo[lst,n]]],{n,6,10!,6}];lst (*...and/or...*) lst={};Do[If[PrimeQ[n-1]&&PrimeQ[n+1],s=(n/5)^(1/2);If[Floor[s]==s,AppendTo[lst,n]]],{n,6,10!,6}];lst
%o (PARI) forstep(k=0,1e4,6, isprime(k^2*5+1) & isprime(k^2*5-1) & print1(k^2*5,",")) \\ _M. F. Hasler_, Apr 11 2009
%Y Cf. A000290, A014574, A154670, A154671, A154673, A154674, A154675, A154676.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 13 2009
%E Edited and extended by _M. F. Hasler_, Apr 11 2009
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