A090430 - OEIS

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A090430

a(n) = if Floor[2*Pi*PrimePi[m]/E] is prime then Floor[2*Pi*PrimePi[m]/E]

2, 11, 13, 23, 41, 43, 53, 67, 71, 73, 83, 97, 101, 113, 127, 131, 157, 173, 191, 233, 251, 263, 277, 281, 293, 307, 337, 349, 353, 367, 379, 383, 397, 409, 439, 443, 457, 487, 499, 503, 547, 557, 563, 577, 587, 607, 617, 619, 631, 647, 661, 677, 691, 709, 739

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,1

COMMENTS

An entropy power function based on the PrimePi distribution with N=n/PrimePi[n].

This function doesn't work as well as n/log(n).

REFERENCES

C. E. Shannon, The Mathematical Theory of Communication, page 93

LINKS

Table of n, a(n) for n=2..56.

MATHEMATICA

digits=25*200 f[n_]=Floor[2*Pi*PrimePi[n]/E] a=Delete[Union[Table[If [PrimeQ[f[n]]==True, f[n], 0], {n, 2, digits}]], 1]