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Number of primes between the n-th squared twin prime pair.
4

%I #6 Nov 10 2017 11:10:52

%S 5,6,9,11,16,20,32,30,42,42,49,58,76,77,75,82,90,91,99,107,125,151,

%T 151,145,165,189,168,189,194,211,241,244,246,259,262,290,304,300,311,

%U 314

%N Number of primes between the n-th squared twin prime pair.

%C a(n) = SUM(A010051(k): A006512(n)^2 <= k <= A001359(n)^2) =

%C A000720(A006512(n)^2)-A000720(A001359(n)^2).

%H Harvey P. Dale, <a href="/A137859/b137859.txt">Table of n, a(n) for n = 1..1000</a>

%e a(4) = #{293,307,311,313,317,331,337,347,349,353,359} = 11.

%t PrimePi[#[[2]]^2]-PrimePi[#[[1]]^2]&/@Select[Partition[ Prime[ Range[ 200]],2,1],#[[2]]-#[[1]]==2&] (* _Harvey P. Dale_, Nov 10 2017 *)

%Y Cf. A079629, A137860.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Feb 16 2008