[seqfan] Re: Concerning A178668.

Maximilian Hasler maximilian.hasler at gmail.com
Mon Jan 3 18:37:10 CET 2011

I think the motivation for replacing 2 and 3 in the much more natural
oeis.org/A060210 should be explained.

Concerning conjectures, if the experimental data leading to these is
given at the same time as explanation, the reader can more easily make
himself an opinion on the probability of its truth.
(100 terms in sequences growing as slowly as the twin primes are not
representative at all.
Since it takes about 0.5 sec to compute 10 000 terms of A060210,
it is somehow a lack of respect to publish an assumption based on 100 terms.)

Finally, the statements should be clearly understandable.
In the present case, I cannot figure out (*) what means "it occurs for
the first time" in

".... the number N for which it occurs for the first time is very large."

In case of difficulties with the English language,
a mathematical "formula" or statement ("N such that a(N) is in Axxxx",
or the like)
makes things completely clear and does not require knowledge of many
English words.

For the sequence at hand, maybe the high frequency of the largest
divisor being a twin prime simply comes from the fact that among the
first 20 odd primes, only 5 are not twin primes...

Below the count of cases where A060210(n) is a twin prime > 3, for n=1..N,
and the number of cases where it is not.

N=100:  [74, 26]  (as opposed to the author's 78+12)
N=10^3: [559, 441]
N=10^4: [4138, 5862]
N=10^5: [33432, 66568]

(*) maybe I now understand the author's "N where it occurs for the
first time", it could meand the N > 16 for which the positive cases
becomes less frequent than the negative ones - it occurs for N=2007
with 1003 positive and 1004 negative cases.

N=10^5; c=0; p=3; for(k=1,N, until(o+2==p,p=nextprime(2+o=p));
a=vecmax(factor(p-1)[,1]); a>3|next; isprime(a+2) | isprime(a-2) |
next; c++*2<k & k>16 & error("Happy New "k)); [c,N-c]

  ***   user error: Happy New 2011

On Mon, Jan 3, 2011 at 11:04 AM, N. J. A. Sloane <njas at research.att.com> wrote:
> JJ asked:
>> I'd like to have advice for situations like this,
> where the OEIS is used as a scratchpad for ongoing
> investigations (of questionable quality)
> Me:
> (I will ignore "of questionable quality for now)
> I think this is an acceptable use of the OEIS, and something
> I have done myself quite often.
> One is trying to understand a sequence S. It seems difficult.
> So one computes various sequences that are derived from it,
> and which look simpler than S. Then it is reasonable to put
> a few of them into the OEIS also, in the hope
> that one day someone will explain them, or discover them
> in a different context.
> So my answer is Yes, it is OK to do this.
> Neil
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