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

0,5

Comments

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

Links

Table of n, a(n) for n=0..111.

Ilya Gutkovskiy, Extended graphical example

Index entries for sequences related to compositions

Formula

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

Example

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)).

Mathematica

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

Crossrefs

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

Sequence in context: A003263 A271224 A157242 * A256626 A135211 A029294

Adjacent sequences: A281420 A281421 A281422 * A281424 A281425 A281426

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 21 2017

Status

approved