[seqfan] The Jacob's Ladder sequence: nice but not new

Neil Sloane njasloane at gmail.com
Tue Feb 20 17:25:32 CET 2018


Dear Seq Fans, the recent arXiv paper

Alberto Fraile, Roberto Martínez, and Daniel Fernández, Jacob's Ladder:
Prime numbers in 2d, arXiv preprint arXiv:1801.01540, 2017

describes a very nice sequence. It would have been a candidate for A300000
except that it was entered in the OEIS in 2001 by Jason Earls, see A065358:
a(n) = Sum_{k=1..n} (-1)^pi(k).

I assume the authors ignored the basic rule about consulting the OEIS:
always omit the first term.

The graph of the sequences is very nice (*).  The places where
it crosses the x-axis are listed in A064940 (in Jason's version), and in
A299300 (add 1 to A064940) in their version.

The reason I'm writing is to ask if someone could extend the b-file for
A064940. It will be necessary to go out to n=20*10^6 or even 100*10^6 to
get a lot of terms.  How many terms do we want in the b-file?  Well, 10K
would be nice, or even 50K!

(*) This is an illustration of the coin-tossing paradox beautifully
described in Feller, Vol 1, Chapter III.  See also "arcsine law".


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