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Number of distinct pairs of externally tangent circles with radius sqrt(2) and center (p,q) where p and q are prime, p + q = A187797(n) and p <= q.
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%I #6 Aug 15 2020 12:56:14

%S 1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,2,1,2,2,1,1,1,3,2,1,2,1,1,2,2,1,2,

%T 2,3,1,3,1,1,2,1,3,1,2,6,1,3,1,1,2,4,1,3,4,4,1,3,1,1,3,1,5,2,6,1,3,1,

%U 2,2,5,2,5,2,1,3,1,2,3,5,2,4,3,1,6,1,2,3,1,3,1,5,1,5,1

%N Number of distinct pairs of externally tangent circles with radius sqrt(2) and center (p,q) where p and q are prime, p + q = A187797(n) and p <= q.

%t Table[If[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[2n - i] - PrimePi[2n - i - 1]) (PrimePi[i - 2] - PrimePi[i - 3]) (PrimePi[2n - i + 2] -PrimePi[2n - i + 1]), {i, 3, n}] > 0, Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[2n - i] - PrimePi[2n - i - 1]) (PrimePi[i - 2] - PrimePi[i - 3]) (PrimePi[2n - i + 2] - PrimePi[2n - i + 1]), {i, 3, n}], {}], {n, 300}] // Flatten

%Y Cf. A187797, A302231.

%K nonn

%O 1,11

%A _Wesley Ivan Hurt_, Aug 11 2020