A089679 - OEIS

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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.

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

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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.

LINKS

Table of n, a(n) for n=1..105.

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

Adjacent sequences: A089676 A089677 A089678 * A089680 A089681 A089682

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Jan 04 2004

STATUS

approved