Half joke half serious generating function for the primes A000040

[N A]

I've recently found a video online about a prime generator called Willans' formula. I've posted a picture from Wolfram MathWorld of it below.

My question is, seeing that OEIS is meant to serve as a reference for formal mathematics research, would it be inappropriate to add to A000040 the formal power series generating function:
G(x) = Sum_{n>=1} [ 1 + Sum_{m=1..2^n} floor( ( n / Sum_{j=1..m} floor(cos^2(π((j−1)!+1)/j)) )^(1/n) ) ] x^n

I ask because this looks rather messy.

Thank you,

Nour Abouyoussef

[Sean A. Irvine]

No. The primes are a "core" sequence so we want to be very selective about which information we include.

Sean.

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[Fred Lunnon]

  I think Sean meant "Yes" (it would be inappropriate)!    WFL 

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[N A]

Good to know and ask, thank you both!
Nour Abouyoussef

[M F Hasler]

The reference / LINK

C. P. Willans, On formulae for the nth prime, Math. Gazette 48 (1964), 413-415.

is already in A000040.

Since the original publisher doesn't give the PDF to anyone, I propose to add the stor.org/stable/3611701 link.

-Maximilian

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