[seqfan] Re: Rounding in A075465

[Robert G. Wilson v]

et al,

	I ran the following two versions of Mathematica:
Round[ Accumulate[ Prime[ Range[1000]]]/Range[1000]];
rnd[n_] := Block[{ip = IntegerPart[n]}, If[n > ip + 1/2, ip + 1, ip]];; r = Range at 1000; rnd@# & /@ (Accumulate[Prime[r]]/r);

	I then compared their results;  they were identical. BUT if the range was increased to 10000, they differ.

	In fact that differ at: 1810, 2458, 240926, 317602, ..., .

	Therefore I suggest that the Mathematica coding in A075465 be changed.

Bob.

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of israel at math.ubc.ca
Sent: Friday, October 02, 2015 6:27 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: Rounding in A075465

Harvey:
Would you mind making that modification to your existing Mathematica code in A075465?
Cheers,
Robert

On Oct 2 2015, Harvey P. Dale wrote:

>        It may be of some passing interest that Mathematica's "Round" 
> function does not always round down in the case of a tie. Instead, the 
> documentation says that "Round rounds numbers of the form x.5 toward 
> the nearest even integer." That means (1) that Mathematica rounds up 
> or down, in the case of a tie, to whichever is the nearest even 
> integer, and (2) that if one wants to control the rounding in 
> Mathematica to be consistent one has to write a separate function to 
> do it correctly. Best, Harvey
> 
>
> -----Original Message----- From: SeqFan 
> [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil Sloane Sent:
> Friday, October 2, 2015 8:08 AM To: Sequence Fanatics Discussion list 
> <seqfan at list.seqfan.eu> Subject: [seqfan] Re: Rounding in A075465
>
>Unless Zak responds otherwise, I suggest we add a comment saying:
>
>In case of a tie, round down.
>
>That is consistent with the data, and is the usual convention anyway.
>
>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 Fri, Oct 2, 2015 at 2:55 AM, <israel at math.ubc.ca> wrote:
>
>> A075465 is "Rounded average of first n primes", but nowhere does it 
>> say what type of rounding is used in case of a tie (i.e. when the 
>> actual average is half an odd integer). Since the Data gives a(2) = 
>> 2,
>> 5/2 is being rounded to 2 rather than 3. That could indicate that 
>> ties are rounded down, or that ties are rounded to the nearest even 
>> integer. The next places the issue will arise in this sequence are
>> a(1810) (which could be 7265 or
>> 7266) and and a(2458) (10285 or 10286).
>>
>> Cheers, Robert
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
>_______________________________________________
>
>Seqfan Mailing list - http://list.seqfan.eu/
>
>_______________________________________________
>
>Seqfan Mailing list - http://list.seqfan.eu/
>
>

_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/