[seqfan] Re: Density of de Polignac numbers

[Tomasz Ordowski]

P.S. The proportion of odd numbers:
2 exp(-2 / log 2) = 0,111666... Nice!
This is the density by my conjecture.
But we're still below 0.1 numerically.

niedz., 31 sty 2021 o 14:14 Tomasz Ordowski <tomaszordowski at gmail.com>
napisał(a):

> Dear readers!
>
> Wesolowski inequality in A254248
> works only for some constant c <= 0.
> For c = 0 we get density d < 1/e correctly.
>
> I found a more sensible formula, namely.
>
> The density d(n) of de Polignac numbers <= n
> is d(n) < (1 - 2 / log n)^(log n / log 2). It works!
> Their asymptotic density d(oo) < 0.055833...
>
> Conjecture: d(n) ~ (1 - 2 / log n)^(log n / log 2).
> The asymptotic density d(oo) = exp(-2 / log 2).
> This density d = 0.055833... is hypothetical.
>
> Any comments are welcome!
>
> Best regards,
>
> Thomas Ordowski
> ____________________
> https://oeis.org/A254248
> https://oeis.org/history/view?seq=A006285&v=73
> https://math.dartmouth.edu/~carlp/coverbirthtalk.pdf
>
>