[seqfan] Re: Sum 1/p log p
RGWv
rgwv at rgwv.com
Mon Mar 26 16:09:44 CEST 2012
Et al,
In "Mathematical Constants", Steven R. Finch, page 186-187, the sum 1/(p
ln(p)) -> 1.6366163233… .
While Erdos & Zhang proved that , for any primitive sequence, sum 1/(a_I
ln(a_i)) < 1.84 and Clark strengthened this to < e^gamma.
The estimate 1.6366163233… given here for the prime series is due to
Cohen.
That got me to https://oeis.org/A137245 Decimal expansion of sum 1/(p
*log p) over the primes p=2,3,5,7,11,...
Hope this helps. Bob.
-----Original Message-----
From: Charles Greathouse
Sent: Monday, March 26, 2012 2:43 AM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Sum 1/p log p
Erdos (1989) conjectured that if a(1), a(2), ... is a sequence where
no term divides another, the sum of 1/(a(n) log a(n)) is at most sum
1/(p log p). Is this constant in the OEIS? Is there a good way to
calculate it to high precision?
Charles Greathouse
Analyst/Programmer
Case Western Reserve University
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