[math-fun] Every N = p1+p2+p3; pi a palindrome
FYI -- This result may have been discussed here already... https://arxiv.org/abs/1602.06208v2 Every positive integer is a sum of three palindromes Javier Cilleruelo, Florian Luca, Lewis Baxter (Submitted on 19 Feb 2016 (v1), last revised 17 Jun 2017 (this version, v2)) For integer $g\ge 5$, we prove that any positive integer can be written as a sum of three palindromes in base $g$.
Not sure about here, but Chris Thompson posted it to seqfans in December 2016, which is what prompted me to (eventually) make the web page that provoked the numberphile video that you probably just watched! On Wed, 19 Sep 2018, 15:14 Henry Baker, <hbaker1@pipeline.com> wrote:
FYI --
This result may have been discussed here already...
https://arxiv.org/abs/1602.06208v2
Every positive integer is a sum of three palindromes
Javier Cilleruelo, Florian Luca, Lewis Baxter
(Submitted on 19 Feb 2016 (v1), last revised 17 Jun 2017 (this version, v2))
For integer $g\ge 5$, we prove that any positive integer can be written as a sum of three palindromes in base $g$.
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Although the result has been proved for bases down to 5, it seems to be true for smaller bases as well, but the proof techniques used by Cilleruelo, Luca, and Baxter are hard to adapt to these cases. Perhaps some funster can settle bases 2, 3, or 4. On Wed, Sep 19, 2018 at 11:40 AM Christian Lawson-Perfect < christianperfect@gmail.com> wrote:
Not sure about here, but Chris Thompson posted it to seqfans in December 2016, which is what prompted me to (eventually) make the web page that provoked the numberphile video that you probably just watched!
On Wed, 19 Sep 2018, 15:14 Henry Baker, <hbaker1@pipeline.com> wrote:
FYI --
This result may have been discussed here already...
https://arxiv.org/abs/1602.06208v2
Every positive integer is a sum of three palindromes
Javier Cilleruelo, Florian Luca, Lewis Baxter
(Submitted on 19 Feb 2016 (v1), last revised 17 Jun 2017 (this version, v2))
For integer $g\ge 5$, we prove that any positive integer can be written as a sum of three palindromes in base $g$.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Is 110 counted as a palindrome? --Rich Quoting Allan Wechsler <acwacw@gmail.com>:
Although the result has been proved for bases down to 5, it seems to be true for smaller bases as well, but the proof techniques used by Cilleruelo, Luca, and Baxter are hard to adapt to these cases. Perhaps some funster can settle bases 2, 3, or 4.
On Wed, Sep 19, 2018 at 11:40 AM Christian Lawson-Perfect < christianperfect@gmail.com> wrote:
Not sure about here, but Chris Thompson posted it to seqfans in December 2016, which is what prompted me to (eventually) make the web page that provoked the numberphile video that you probably just watched!
On Wed, 19 Sep 2018, 15:14 Henry Baker, <hbaker1@pipeline.com> wrote:
FYI --
This result may have been discussed here already...
https://arxiv.org/abs/1602.06208v2
Every positive integer is a sum of three palindromes
Javier Cilleruelo, Florian Luca, Lewis Baxter
(Submitted on 19 Feb 2016 (v1), last revised 17 Jun 2017 (this version, v2))
For integer $g\ge 5$, we prove that any positive integer can be written as a sum of three palindromes in base $g$.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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110 is not counted as a palindrome according to the rules adopted by the authors of that paper. In their introduction they stipulate that the leading digit (delta[l-1] in a transcription of their notation) is nonzero. On Wed, Sep 19, 2018 at 12:38 PM <rcs@xmission.com> wrote:
Is 110 counted as a palindrome? --Rich
Quoting Allan Wechsler <acwacw@gmail.com>:
Although the result has been proved for bases down to 5, it seems to be true for smaller bases as well, but the proof techniques used by Cilleruelo, Luca, and Baxter are hard to adapt to these cases. Perhaps some funster can settle bases 2, 3, or 4.
On Wed, Sep 19, 2018 at 11:40 AM Christian Lawson-Perfect < christianperfect@gmail.com> wrote:
Not sure about here, but Chris Thompson posted it to seqfans in December 2016, which is what prompted me to (eventually) make the web page that provoked the numberphile video that you probably just watched!
On Wed, 19 Sep 2018, 15:14 Henry Baker, <hbaker1@pipeline.com> wrote:
FYI --
This result may have been discussed here already...
https://arxiv.org/abs/1602.06208v2
Every positive integer is a sum of three palindromes
Javier Cilleruelo, Florian Luca, Lewis Baxter
(Submitted on 19 Feb 2016 (v1), last revised 17 Jun 2017 (this version, v2))
For integer $g\ge 5$, we prove that any positive integer can be written as a sum of three palindromes in base $g$.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Before we try to prove the conjecture for base 2, can anybody easily do a reality check? Like, is it in fact true for n < 2^30 or so? On Wed, Sep 19, 2018 at 12:57 PM Allan Wechsler <acwacw@gmail.com> wrote:
110 is not counted as a palindrome according to the rules adopted by the authors of that paper. In their introduction they stipulate that the leading digit (delta[l-1] in a transcription of their notation) is nonzero.
On Wed, Sep 19, 2018 at 12:38 PM <rcs@xmission.com> wrote:
Is 110 counted as a palindrome? --Rich
Quoting Allan Wechsler <acwacw@gmail.com>:
Although the result has been proved for bases down to 5, it seems to be true for smaller bases as well, but the proof techniques used by Cilleruelo, Luca, and Baxter are hard to adapt to these cases. Perhaps some funster can settle bases 2, 3, or 4.
On Wed, Sep 19, 2018 at 11:40 AM Christian Lawson-Perfect < christianperfect@gmail.com> wrote:
Not sure about here, but Chris Thompson posted it to seqfans in December 2016, which is what prompted me to (eventually) make the web page that provoked the numberphile video that you probably just watched!
On Wed, 19 Sep 2018, 15:14 Henry Baker, <hbaker1@pipeline.com> wrote:
FYI --
This result may have been discussed here already...
https://arxiv.org/abs/1602.06208v2
Every positive integer is a sum of three palindromes
Javier Cilleruelo, Florian Luca, Lewis Baxter
(Submitted on 19 Feb 2016 (v1), last revised 17 Jun 2017 (this version, v2))
For integer $g\ge 5$, we prove that any positive integer can be written as a sum of three palindromes in base $g$.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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The base 2, 3, 4 cases are already resolved. See https://arxiv.org/abs/1706.10206 On Wed, Sep 19, 2018 at 11:40 AM Allan Wechsler <acwacw@gmail.com> wrote:
Before we try to prove the conjecture for base 2, can anybody easily do a reality check? Like, is it in fact true for n < 2^30 or so?
On Wed, Sep 19, 2018 at 12:57 PM Allan Wechsler <acwacw@gmail.com> wrote:
110 is not counted as a palindrome according to the rules adopted by the authors of that paper. In their introduction they stipulate that the leading digit (delta[l-1] in a transcription of their notation) is nonzero.
On Wed, Sep 19, 2018 at 12:38 PM <rcs@xmission.com> wrote:
Is 110 counted as a palindrome? --Rich
Quoting Allan Wechsler <acwacw@gmail.com>:
Although the result has been proved for bases down to 5, it seems to
be
true for smaller bases as well, but the proof techniques used by Cilleruelo, Luca, and Baxter are hard to adapt to these cases. Perhaps some funster can settle bases 2, 3, or 4.
On Wed, Sep 19, 2018 at 11:40 AM Christian Lawson-Perfect < christianperfect@gmail.com> wrote:
Not sure about here, but Chris Thompson posted it to seqfans in December 2016, which is what prompted me to (eventually) make the web page that provoked the numberphile video that you probably just watched!
On Wed, 19 Sep 2018, 15:14 Henry Baker, <hbaker1@pipeline.com> wrote:
FYI --
This result may have been discussed here already...
https://arxiv.org/abs/1602.06208v2
Every positive integer is a sum of three palindromes
Javier Cilleruelo, Florian Luca, Lewis Baxter
(Submitted on 19 Feb 2016 (v1), last revised 17 Jun 2017 (this version, v2))
For integer $g\ge 5$, we prove that any positive integer can be written as a sum of three palindromes in base $g$.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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Oh, excellent. And recent, so I don't feel embarrassed about not knowing it. Punchline: There are numbers that are not the sum of three palindromes in binary -- sometimes you need four, but never more than that. For all higher bases, three palindromes suffices. On Wed, Sep 19, 2018 at 2:47 PM Tom Duff <td@pixar.com> wrote:
The base 2, 3, 4 cases are already resolved. See https://arxiv.org/abs/1706.10206
On Wed, Sep 19, 2018 at 11:40 AM Allan Wechsler <acwacw@gmail.com> wrote:
Before we try to prove the conjecture for base 2, can anybody easily do a reality check? Like, is it in fact true for n < 2^30 or so?
On Wed, Sep 19, 2018 at 12:57 PM Allan Wechsler <acwacw@gmail.com> wrote:
110 is not counted as a palindrome according to the rules adopted by the authors of that paper. In their introduction they stipulate that the leading digit (delta[l-1] in a transcription of their notation) is nonzero.
On Wed, Sep 19, 2018 at 12:38 PM <rcs@xmission.com> wrote:
Is 110 counted as a palindrome? --Rich
Quoting Allan Wechsler <acwacw@gmail.com>:
Although the result has been proved for bases down to 5, it seems to
be
true for smaller bases as well, but the proof techniques used by Cilleruelo, Luca, and Baxter are hard to adapt to these cases. Perhaps some funster can settle bases 2, 3, or 4.
On Wed, Sep 19, 2018 at 11:40 AM Christian Lawson-Perfect < christianperfect@gmail.com> wrote:
Not sure about here, but Chris Thompson posted it to seqfans in December 2016, which is what prompted me to (eventually) make the web page that provoked the numberphile video that you probably just watched!
On Wed, 19 Sep 2018, 15:14 Henry Baker, <hbaker1@pipeline.com> wrote:
> FYI -- > > This result may have been discussed here already... > > https://arxiv.org/abs/1602.06208v2 > > Every positive integer is a sum of three palindromes > > Javier Cilleruelo, Florian Luca, Lewis Baxter > > (Submitted on 19 Feb 2016 (v1), last revised 17 Jun 2017 (this version, > v2)) > > For integer $g\ge 5$, we prove that any positive integer can be written as > a sum of three palindromes in base $g$. > > > _______________________________________________ > math-fun mailing list > math-fun@mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (5)
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Allan Wechsler -
Christian Lawson-Perfect -
Henry Baker -
rcs＠xmission.com -
Tom Duff