A089687 Linear chaotic function based on log function from primes and prime distribution.

5, 4, 6, 6, 8, 7, 8, 11, 14, 12, 15, 13, 14, 16, 19, 18, 19, 18, 19, 20, 23, 20, 23, 26, 28, 29, 31, 27, 28, 29, 31, 34, 34, 39, 40, 37, 39, 41, 44, 40, 41, 40, 40, 42, 43, 42, 47, 48, 49, 51, 54, 48, 52, 55, 57, 60, 61, 56, 58, 52, 56, 62, 63, 64, 66, 64, 67, 71, 72, 66, 69, 65

Offset

2,1

Comments

Based on function solution of: Solve[(Prime[n]+a*PrimePi[n])/(1+a)-Sqrt[Prime[n]*PrimePi[n]]=0,a] which gives a log type function a[n].

Links

Table of n, a(n) for n=2..73.

Formula

a(n) = floor(exp((prime(n) - sqrt(prime(n)* primepi(n)))/(-primepi(n) + sqrt(prime(n)* primepi(n))))).

Mathematica

digits=200; b = Table[Floor[Exp[(Prime[n] - Sqrt[Prime[n]* PrimePi[n]])/(-PrimePi[n] + Sqrt[Prime[n]* PrimePi[n]])]], {n, 2, digits}]

Crossrefs

Sequence in context: A138255 A153451 A190143 * A251792 A159894 A011502

Adjacent sequences: A089684 A089685 A089686 * A089688 A089689 A089690

Keyword

nonn,uned

Author

Roger L. Bagula, Jan 05 2004

Status

approved