A281423 Expansion of (Sum_{k>=1} x^prime(prime(k)))^2 [even terms only].
0, 0, 0, 1, 2, 1, 0, 2, 2, 0, 2, 3, 0, 0, 2, 0, 0, 3, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 2, 0, 3, 2, 0, 0, 4, 4, 0, 2, 2, 0, 1, 2, 2, 2, 2, 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, 2, 4, 0, 1, 2, 0, 2, 4, 0, 2, 2, 1, 0, 2, 2, 2, 2, 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, 1, 6, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 4, 4, 2, 0, 2, 0, 0, 2, 4, 0, 2, 4, 1, 2, 4
Offset: 0
Keywords
Examples
a(4) = 2 because we have [3, 5] and [5, 3], where 3 = prime(2) = prime(prime(1)) and 5 = prime(3) = prime(prime(2)).
Links
Programs
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Mathematica
Take[CoefficientList[Series[Sum[x^Prime[Prime[k]], {k, 1, 250}]^2, {x, 0, 250}], x], {1, -1, 2}]
Formula
G.f.: (Sum_{k>=1} x^prime(prime(k)))^2 [even terms only].
Comments