[seqfan] Re: A071196

[M. F. Hasler]

I don't think that we can prove it deterministically, but the probability
that for some prime you can add infinitely many subsequent primes without
ever getting a prime is zero.

But I'm intrigued by the scatterplot for A071194.
Obviously the sequence contains after the initial 2 only odd numbers > 2.
According to my analysis which appears confirmed by the b-file, all odd
numbers occur, with frequency decreasing with their size.
(See PARI code below.)
However, the scatterplot appears to show empty horizontal lines as if every
third odd number would not occur.

Can anyone explain this?

- Maximilian
(PARI)
m=Map(); forprime(p=1,20000, mapput(m,t=a(,p), iferr( mapget(m,t)+1,
E,1))); m
%4 = Map([2, 1; 3, 669; 5, 397; 7, 235; 9, 157; 11, 138; 13, 94; 15, 81;
17, 74; 19, 65; 21, 53; 23, 40; 25, 34; 27, 33; 29, 23; 31, 14; 33, 19; 35,
19; 37, 16; 39, 21; 41, 11; 43, 10; 45, 5; 47, 7; 49, 8; 51, 3; 53, 6; 55,
6; 57, 3; 59, 3; 61, 1; 63, 2; 65, 2; 69, 2; 75, 1; 77, 2; 79, 1; 81, 1;
83, 1; 85, 1; 87, 1; 95, 2])

On Tue, 17 Nov 2020, 12:47 Neil Sloane, <njasloane at gmail.com> wrote:

> Emmanuel asks if we know that A071196(n) exists.  As far as I know, the
> answer is no. The same question applies to all of A071194, -95, etc.,
> Unless someone knows of a proof (Charles Greathouse, perhaps?), I will add
> an escape clause (as usual by defining the value to be -1 if ... does not
> exist)
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
>
> On Tue, Nov 17, 2020 at 11:36 AM Emmanuel Vantieghem <
> emmanuelvantieghem at gmail.com> wrote:
>
> > L.S,
> >
> > Is it proved somewhere that  A071196 <https://oeis.org/A071196>(n)  is
> > defined for every  n ?
> > Or is this a conjecture ?
> >
> > Emmanuel.
>