A090417 Primes of the form floor(2*Pi*n/(e*log(n))).

7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281

Offset: 1

Author

Roger L. Bagula, Jan 31 2004

Keywords

• nonn
• easy
• changed

Comments

An entropy power of white noise function with N=1/log(n).

Function is based on asymptotic form of distribution: PrimePi[n]--> n/log(n) Function misses the first three primes {2,3,5}, but is pretty good after that.

It is easy to see due to the slow growth of the function that the sequence is precisely the primes greater than 5. [Charles R Greathouse IV, Aug 21 2011]

References

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

Crossrefs

Cf. A004139.

Programs

Mathematica

digits=5*200 f[n_]=Floor[2*Pi*n/(E*Log[n])] a=Delete[Union[Table[If [PrimeQ[f[n]]==True, f[n], 0], {n, 2, digits}]], 1]

PARI

a(n)=prime(n+3) \\ Charles R Greathouse IV, Aug 21 2011