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User talk:Peter Luschny/RiemannLagarias

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well, in course of searching for something, ended up at your webpage and eventually to your OEIS wikipage. I saw you mention/work with the Lagarias equivalent.
It's been a long time but I recall working up what I thought was an equiv to Lagarias involving the half-harmonic

from my 2008 notes (which I actually don't fully follow now!),

exp(AQ)< exp(H)ln(H) for ln(sigma)~ A*Q +B
where B<=ln(2), A<=1 required (strictly)
H=harmonic# N and Q=harmonic # (N/2)

for N>=7207200, the (0 intercept) slopes ln(sigma)/Q seem to be <1 ie due to B>0, lower N can accomodate
observation shows that ln(sigma)/Q can increase or decrease with increasing N

I am sure I must have coded it in Pari at some point. I share only if it's of any interest, else sorry for the bother--Bill McEachen 03:25, 14 February 2011 (UTC)