A090416 a(n) = if Floor[(2*Pi/E)*m] is prime then Floor[(2*Pi/E)*m]

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

Offset

1,1

Comments

Primes that behave like Shannon entropy power white noise with n=1.

Since (2*Pi/E) is a transcendental irrational, this function is a kind of irrational rotation related function, that is: Mod[(2*Pi/E)*n,1] is an irrational rotation and these numbers are Beatty in type such that: Beatty number+ irrational rotation =n Of my experiments in white noise entropy powers N=2 gives the most primes

References

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

Links

Table of n, a(n) for n=1..55.

Mathematica

digits=5*200 f[n_]=Floor[(2*Pi/E)*n] a=Delete[Union[Table[If [PrimeQ[f[n]]==True, f[n], 0], {n, 1, digits}]], 1]
With[{c=(2*Pi)/E}, Select[Table[Floor[c*n], {n, 400}], PrimeQ]] (* Harvey P. Dale, Mar 31 2024 *)

Crossrefs

Sequence in context: A045384 A191075 A045385 * A090430 A363215 A022115

Adjacent sequences: A090413 A090414 A090415 * A090417 A090418 A090419

Keyword

nonn

Author

Roger L. Bagula, Jan 31 2004

Status

approved