[seqfan] Re: A071196
israel at math.ubc.ca
israel at math.ubc.ca
Wed Nov 18 05:08:38 CET 2020
I think this is an "aliasing" effect, due to the fact the distance between
what should be the y coordinates of the odd numbers is not an integer
number of pixels. Thus in some cases the "+"'s representing the points for
y and y+2 are placed far enough apart that you can see white space between
them, in other cases you can't.
Cheers,
Robert
On Nov 17 2020, M. F. Hasler wrote:
>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.
>>
>
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>
>
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