[math-fun] Multiply my digits
5 terms (with my smartphone)! 6,16,144,1944,3899,... Best, É.
6 terms: [6, 32, 48, 168, 27216, 666792] 7 terms: [20, 54, 336, 768, 2688, 27648, 826686] altermative 7 terms: [20, 54, 336, 768, 2688, 27648, 2239488] 8 terms: [20, 54, 336, 768, 2688, 27648, 338688, 4478976] Obtained using Maple's GraphTheory Package. I think this is the best one can do using only 7-smooth numbers <http://oeis.org/A002473> up to 10 million On Fri, Jul 26, 2019 at 2:30 AM Éric Angelini <eric.angelini@skynet.be> wrote:
5 terms (with my smartphone)! 6,16,144,1944,3899,... Best, É.
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What about A3001? The smallest number of multiplicative persistence n. 0, 10, 25, 39, 77, 679, 6788, 68889, 2677889, 26888999, 3778888999, 277777788888899 See A121111 for the last term: 277777788888899, 4996238671872, 438939648, 4478976, 338688, 27648, 2688, 768, 336, 54, 20, 0 (read it backwards to get your problem) I found this in 1973, and conjectured that 11 steps is the largest possible. The conjecture has is still open (but certainly true) 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@gmail.com On Fri, Jul 26, 2019 at 2:41 PM W. Edwin Clark <wclark@mail.usf.edu> wrote:
6 terms: [6, 32, 48, 168, 27216, 666792] 7 terms: [20, 54, 336, 768, 2688, 27648, 826686] altermative 7 terms: [20, 54, 336, 768, 2688, 27648, 2239488] 8 terms: [20, 54, 336, 768, 2688, 27648, 338688, 4478976] Obtained using Maple's GraphTheory Package. I think this is the best one can do using only 7-smooth numbers <http://oeis.org/A002473> up to 10 million
On Fri, Jul 26, 2019 at 2:30 AM Éric Angelini <eric.angelini@skynet.be> wrote:
5 terms (with my smartphone)! 6,16,144,1944,3899,... Best, É.
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Why 1944 and not 1449? On Fri, Jul 26, 2019 at 12:30 AM Éric Angelini <eric.angelini@skynet.be> wrote:
5 terms (with my smartphone)! 6,16,144,1944,3899,... Best, É.
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Because 1449=3^2*7*23 is not 7-smooth, so it does not permit an extension. On Fri, Jul 26, 2019, 5:27 PM Mike Stay <metaweta@gmail.com> wrote:
Why 1944 and not 1449?
On Fri, Jul 26, 2019 at 12:30 AM Éric Angelini <eric.angelini@skynet.be> wrote:
5 terms (with my smartphone)! 6,16,144,1944,3899,... Best, É.
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-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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I must not understand the rules. Is it not the smallest number whose digits multiply to give the previous one? On Fri, Jul 26, 2019 at 3:57 PM Allan Wechsler <acwacw@gmail.com> wrote:
Because 1449=3^2*7*23 is not 7-smooth, so it does not permit an extension.
On Fri, Jul 26, 2019, 5:27 PM Mike Stay <metaweta@gmail.com> wrote:
Why 1944 and not 1449?
On Fri, Jul 26, 2019 at 12:30 AM Éric Angelini <eric.angelini@skynet.be> wrote:
5 terms (with my smartphone)! 6,16,144,1944,3899,... Best, É.
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-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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By my reading, Eric never insists on the smallest. His very first example starts 8, 42 ... On Fri, Jul 26, 2019, 6:12 PM Mike Stay <metaweta@gmail.com> wrote:
I must not understand the rules. Is it not the smallest number whose digits multiply to give the previous one?
On Fri, Jul 26, 2019 at 3:57 PM Allan Wechsler <acwacw@gmail.com> wrote:
Because 1449=3^2*7*23 is not 7-smooth, so it does not permit an
extension.
On Fri, Jul 26, 2019, 5:27 PM Mike Stay <metaweta@gmail.com> wrote:
Why 1944 and not 1449?
On Fri, Jul 26, 2019 at 12:30 AM Éric Angelini <
eric.angelini@skynet.be>
wrote:
5 terms (with my smartphone)! 6,16,144,1944,3899,... Best, É.
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-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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I see, I missed an earlier message in the thread. On Fri, Jul 26, 2019 at 4:15 PM Allan Wechsler <acwacw@gmail.com> wrote:
By my reading, Eric never insists on the smallest. His very first example starts 8, 42 ...
On Fri, Jul 26, 2019, 6:12 PM Mike Stay <metaweta@gmail.com> wrote:
I must not understand the rules. Is it not the smallest number whose digits multiply to give the previous one?
On Fri, Jul 26, 2019 at 3:57 PM Allan Wechsler <acwacw@gmail.com> wrote:
Because 1449=3^2*7*23 is not 7-smooth, so it does not permit an
extension.
On Fri, Jul 26, 2019, 5:27 PM Mike Stay <metaweta@gmail.com> wrote:
Why 1944 and not 1449?
On Fri, Jul 26, 2019 at 12:30 AM Éric Angelini <
eric.angelini@skynet.be>
wrote:
5 terms (with my smartphone)! 6,16,144,1944,3899,... Best, É.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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participants (5)
-
Allan Wechsler -
Mike Stay -
Neil Sloane -
W. Edwin Clark -
Éric Angelini