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A090417 Primes of the form floor(2*Pi*n/(e*log(n))). 1

%I #10 May 13 2013 01:48:20

%S 7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,

%T 103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,

%U 193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281

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

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

%C 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.

%C 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]

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

%t 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]

%o (PARI) a(n)=prime(n+3) \\ _Charles R Greathouse IV_, Aug 21 2011

%K nonn,easy

%O 1,1

%A _Roger L. Bagula_, Jan 31 2004

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Last modified November 30 05:42 EST 2023. Contains 367454 sequences. (Running on oeis4.)