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A089679
Let g[n_]=Floor[(Prime[n]-n)/(n-PrimePi[n])]. Then a(n) = (g[n]+g[n+1])-g[n*(n+1)]+1.
0
2, 2, 1, 1, 2, 2, 1, 0, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1
OFFSET
1,1
COMMENTS
Log-type weighted average function of primes and the prime distribution.
This function makes use of the addition property of logs. The resulting function looks like a log square wave with ringing on the leading edge.
MATHEMATICA
digits=200 g[n_]=Floor[(Prime[n]-n)/(n-PrimePi[n])] b=Table[(g[n]+g[n+1])-g[n*(n+1)]+1, {n, 1, digits}]
CROSSREFS
Sequence in context: A131852 A139352 A214039 * A290320 A348761 A318703
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Jan 04 2004
STATUS
approved