[seqfan] Re: Numbers > 1 not multiple nor a sum of any other terms.

[jnthn stdhr]

@Neil Sloane: The name in A330071 isn't correct, as the terms in that seq.
aren't found in A330070, no?

On Sun, Dec 1, 2019 at 4:51 PM Neil Sloane <njasloane at gmail.com> wrote:

> I've edited both A330070 and A330071.
>
> 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 Sun, Dec 1, 2019 at 1:12 PM Neil Sloane <njasloane at gmail.com> wrote:
>
> > David Seal makes some excellent comments and indeed the definition should
> > be clarified in the way he suggests.
> >
> > As for "lexicographically earliest sequences " versus "a(n) is the
> > smallest number such that ...", remember these are different conditions:
> > the former is a global condition, the latter is a local condition. It
> > probably doesn't matter here, so let's use "greedy", which is a lot
> simpler.
> >
> > The point is that "lex earliest" allows backtracking, whereas "a(n) is
> > smallest" uses the greedy algorithm and doesn't let you correct mistakes
> if
> > you run into a dead end. Example: A327762 uses greedy alg and dies after
> 56
> > terms, while A327460 is lex earliest and is infinite.
> >
> > Jonathan, will you make the necessary changes to your submission?
> >
> > 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 Sun, Dec 1, 2019 at 10:23 AM Christian Lawson-Perfect <
> > christianperfect at gmail.com> wrote:
> >
> >> A similarly naive Python script produced the following 31 terms in a few
> >> seconds, then ran out of memory:
> >>
> >> 2, 3, 7, 11, 17, 25, 59, 67, 185, 193, 563, 571, 1697, 1747, 5141, 5149,
> >> 11995, 25727, 27439, 78893, 82345, 240131, 243583, 723845, 727297,
> >> 2174987,
> >> 2178439, 6530119, 6530123, 13061947, 19590377
> >>
> >> On Sun, 1 Dec 2019 at 09:46, jnthn stdhr <jstdhr at gmail.com> wrote:
> >>
> >> > Hi all.
> >> >
> >> > I didn't find this in the db, and superseeker had no suggestions.
> >> > https://oeis.org/A330070 is the sequence of numbers that are neither
> a
> >> sum
> >> > nor a multiple of smaller terms, and starts:
> >> >
> >> > 2, 3, 7, 11, 17, 25, 59, 67, 185, 193, 563, 571, 1697, 1747, 5141,
> 5149,
> >> > 11995, 25727, 27439, 78893, 82345, 240131, 243583,...
> >> >
> >> > Example:  a(6) = 25, because 25 = 5 x 5, and 5 is not in the sequence,
> >> and
> >> > no combination of 2, 3, 7, 11, and 17 sum to 25.
> >> >
> >> > The divisors (d > 1) of composite terms are:
> >> >
> >> > 25 [5]
> >> > 185 [5, 37]
> >> > 5141 [53, 97]
> >> > 5149 [19, 271]
> >> > 11995 [5, 2399]
> >> > 25727 [13, 1979]
> >> > 27439 [23, 1193]
> >> > 82345 [5, 16469, 43, 1915, 215, 383]
> >> >
> >> > Based on my original idea below (composites with this property), my
> >> > conjecture is that composite terms > 25  will only have either two or
> >> six
> >> > non-trivial divisors.
> >> >
> >> > My code takes ten+ minutes to find the first 21 terms.  The "is n a
> >> > multiple" test is efficient enough, just test if any divisors of n are
> >> in
> >> > the sequence.  As for sums, naively, I am storing all combinations,
> >> which
> >> > means in the worst case ~2^n sums must be checked.  Any ideas on how
> to
> >> > improve on this?
> >> >
> >> > A330071 will be the composite-only version, if that seems appropriate.
> >> > 4, 6, 9, 14, 21, 22, 38, 106, 111, 118,123, 465, 470,1394, 1405, 4193,
> >> > 4209, 9446,13289, 22258, 26101, 70617, 79959, ...
> >> >
> >> > divisors > 1:
> >> > 4 [2]
> >> > 6 [2, 3]
> >> > 9 [3]
> >> > 14 [2, 7]
> >> > 21 [3, 7]
> >> > 22 [2, 11]
> >> > 38 [2, 19]
> >> > 106 [2, 53]
> >> > 111 [3, 37]
> >> > 118 [2, 59]
> >> > 123 [3, 41]
> >> > 465 [3, 155, 5, 93, 15, 31]
> >> > 470 [2, 235, 5, 94, 10, 47]
> >> > 1394 [2, 697, 17, 82, 34, 41]
> >> > 1405 [5, 281]
> >> > 4193 [7, 599]
> >> > 4209 [3, 1403, 23, 183, 61, 69]
> >> > 9446 [2, 4723]
> >> > 13289 [97, 137]
> >> > 22258 [2, 11129, 31, 718, 62, 359]
> >> > 26101 [43, 607]
> >> > 70617 [3, 23539]
> >> > 79959 [3, 26653, 11, 7269, 33, 2423]
> >> >
> >> >  For this one, super seeker suggested  (lgdegf)
> >> > 81-216*a(n)+216*a(n)^2-96*a(n)^3+16*a(n)^4.
> >> >
> >> > Jonathan
> >> >
> >> > --
> >> > Seqfan Mailing list - http://list.seqfan.eu/
> >> >
> >>
> >> --
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >
>
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