[seqfan] Re: how is A177018 defined?
chris.eveswell at virgin.net
Sat Jun 19 21:24:00 CEST 2010
For the values listed in A080370 in the OEIS, the following differences
between q(n) and A080370(n+1) occur:
n A067076 q A080370
24 47 71 66
25 49 74 70
30 62 92 84
31 64 95 90
34 73 107 101
35 74 109 106
42 94 136 130
43 95 138 135
46 104 150 143
47 110 157 149
48 112 160 155
49 113 162 159
50 115 165 161
53 124 177 171
54 127 181 176
55 130 185 180
56 133 189 184
57 134 191 188
From: seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu]
On Behalf Of Marc LeBrun
Sent: 18 June 2010 5:15 PM
To: Sequence Fanatics Discussion list; Richard Mathar
Subject: [seqfan] Re: how is A177018 defined?
The description does seem needlessly opaque. Some comments/suggestions:
* A description of the form "Numbers n such that <predicate on n>."
implies that the sequence is a set (aka "list"). As such it shouldn't
contain duplicated elements. (Also be increasing, have offset=1, etc).
For instance, a good example is A067076.
* In descriptions A-numbers are basically opaque "pointers" and should be
avoided--unless they *significantly* improve clarity--otherwise use text,
preferably something very similar to the description found at that A-number.
Plausible exceptions to this might be when the referenced sequence has a
complicated description, when the referring sequence is very strongly
related or derivative in some way (eg "Record values of...") or when the
resulting text would be too confusing (eg nested conditionals resulting in
complicated dependent clauses, ambiguous pronoun references, etc).
(In fact, in seqfan eMail, I wish people would include at least some brief
explanatory text when introducing a new A-number in a thread. Following
links is a distraction that I suspect often results in ignored queries.)
* Conversely, it's reasonable to refer to A-numbers in formulas etc. (Of
course every such A-number should then appear in the "see also" list too).
* Also, an A-number refers to an entire sequence. Since the OEIS
contains both sequences that are sets and sequences that are maps notations
such as A067076+A001477 might potentially mean many things, including:
the union of their members
the sequence formed by summing corresponding sequence elements
the set of distinct sums of corresponding elements
the set of distinct pairwise sums
the table of every pairwise sum
* In particular, the reference to A001477 seems especially obfuscatory,
and the presence of n in the same expression renders it unintelligible.
* If I understand it, the code seems to be generating a pair of
non-decreasing sequences, which I'll notate a(n) and c(n), such that
p(n) := a(n) + c(n) + A067076[c(n)]
is always an odd prime.
The algorithm travels from (0,0) in the (a,c) grid: when p(n) is an odd
prime it outputs the a coordinate and steps in the c direction, otherwise it
steps in the a direction.
While I don't get the motivation for this, I observe that the condition
implicitly references the sequence
q(n) := p(n) - a(n) = n + A067076[n]
(Yow, is q = A080370?! Sorry, I'm working by hand. Anyway, if it isn't
already we should put it in the OEIS)
Given q(n) I suspect it might be possible to compose a reasonably
comprehensible description of a(n), but I'm out of steam for now...
>="Maximilian Hasler" <maximilian.hasler at gmail.com>
> The sequence is created by the following code, which I tried to make
> as clear as possible:
> n=0; c=0;for(i=1,99, t = n+c+A067076(c); if( t%2 == 1 && isprime(t),
> print1(n", "); c++,/*else*/ n++ ))
> 3, 3, 3, 4, 4, 5, 5, 6, 8, 8, 10, 11, 11, 12, 14, 16, 16, 18, 19, 19,
> 21, 22, 24, 27, 28, 28, 29, 29, 30, 36, 37, 39, 39, 43, 43, 45, 47,
> 48, 50, 52, 52, 56, 56,
> On Fri, Jun 18, 2010 at 8:50 AM, Richard Mathar
> <mathar at strw.leidenuniv.nl> wrote:
>> I have problems understanding the (apparently simple)
>> "Numbers n such that n+A067076+A001477 is odd prime"
>> Why are values occurring more than once?
>> Which indices (or index combinations) are missing in the definition?
>> If we use "Numbers n such that n+A067076(n)+A001477(n) is prime",
>> which is of course the same as
>> "Numbers n such that 2n+A067076(n) is prime"
>> we get the very different
>> Lead by the examples I considered "Smallest k such that
>> k+A067076(n+1)+A001477(n) is an odd prime"
>> but this doesn't match either.
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