[seqfan] Re: New Prime Curio about 199 by Post

[Rick Shepherd]

Hello.  My suggestion is to submit the pair of sequences as you have
them, your third
and fourth columns as given -- but begin with offset n=0 in each case to
increase the
likelihood of a search finding them.  Note that in your last row the 4
should be a 3
(not counting the 211).  Please double-check that your intervals are defined
the
way you mean for them to be.  All your other terms are consistent with the
intervals
as you twice stated them.  I've checked that neither sequence (beginning
with offset
0 or with offset 199) is currently in the OEIS.  See related discussion and
the terms
I calculated with PARI below.

Regarding the #primes of the form 3x+1 in such intervals, that sequence has
terms
greater than 0 for n>=112 (the other form requires the 199).

Several years ago I casually mentioned to Neil that in some cases it might
be
desirable to have different cross-referenced entries for the *same* sequence
in the
database with offsets such that one continues where the other leaves off --
in order
to ease the search process.  Although I have no strong opinion about this
suggestion,
there may be cases that warrant that (if this could be done in a way that
avoids confusion).
In this context, that could mean having the sequence starting with index 199
(or 112) also.
Another idea would be to have the sequences contain two or three hundred
terms each
in this case (if, for example, 199 is "well-known").  Having said all this,
the possibility of
b-files now may make the above less desirable.  This would especially be
true if the b-files
themselves were searchable exactly as if they were part of their main
entries (when/if that
ever becomes practical).

For what it's worth.

Regards,
Rick

Here are 350 terms of each beginning with offset 0:

#3x - 1
PARI code:   a3xm1(n) =
c=0;lim=floor(8/7*n);for(k=n+1,lim,if(isprime(k)&&(k%3==2),c++));c

0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1,
1,1,2,1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,3,
3,2,2,2,2,2,2,1,1,1,1,1,1,0,0,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,2,2,1,
1,1,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,2,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,0,0,1,
1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,4,4,4,4,5,5,4,4,4,5,5,5,4,4,4,4,4,4,4,5,5,5,5,
5,4,4,4,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,2,2,2,2,3,3,3,3,3,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,
2,2,2,2,3,3,3,3,3,4,4,3,3,3,3,4,4,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,4,4,4

#3x + 1
PARI code:   a3xp1(n) =
c=0;lim=floor(8/7*n);for(k=n+1,lim,if(isprime(k)&&(k%3==1),c++));c

0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,1,1,0,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,
0,0,0,0,1,1,1,1,1,2,2,1,1,1,2,2,2,1,1,1,2,2,2,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,3,2,2,2,
2,2,2,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,1,1,1,1,1,1,2,2,2,2,2,3,2,2,2,2,3,3,3,3,3,3,3,
3,2,2,2,2,2,2,1,1,2,2,2,2,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,2,2,2,2,3,3,3,3,3,3,3,3,2,2,2,3,3,3,2,
2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,2,2,2,1,1,2,2,2,2,2,3,3,
3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,3,3,3,4,4,4,3,3,3,3,3,3,2,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,
4,4,4,4,4,4,5,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,4,4,4,4,4,5,5,5,5,4,5,5,5,5,5,4,4,4,4,4,4,4,4,4,4,4,5,4