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approved

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<a href="/index/Com#comp">Index entries for sequences related to compositions</a>

<a href="/index/Com#comp">Index entries for sequences related to compositions</a>

Cf. A001031, A002375, A006450, A023360, A045917, A073610, A281422.

Ilya Gutkovskiy, <a href="/A281423/a281423.pdf">Extended graphical example</a>

Cf. A001031, A002375, A006450, A023360, A045917, A006450, A073610, A280917A281422.

allocated for Ilya GutkovskiyExpansion 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

0,5

Number of ways to write 2n as an ordered sum of two primes with prime subscripts (A006450).

<a href="/index/Com#comp">Index entries for sequences related to compositions</a>

G.f.: (Sum_{k>=1} x^prime(prime(k)))^2 [even terms only].

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)).

Take[CoefficientList[Series[Sum[x^Prime[Prime[k]], {k, 1, 250}]^2, {x, 0, 250}], x], {1, -1, 2}]

Cf. A001031, A002375, A006450, A023360, A045917, A006450, A073610, A280917.

allocated

nonn

Ilya Gutkovskiy, Jan 21 2017

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editing

allocated for Ilya Gutkovskiy

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