[math-fun] 1,3,11,13,17,23,73,...
I was surprised to see that the integer sequence 1,3,11,13,17,23,73,... consisting of all the record-breakers in sequence A005589 (i.e., all positive integers whose representation as an English word or phrase is longer than the English representations of all earlier positive integers) isn’t a sequence of its own. Did I make a mistake in computing the list of record-breakers? I actually don’t find such sequences very interesting, but I know others do. In particular, my daughter has asked me to write a blog essay about the fact that repeatedly applying the map k->A005589 <http://oeis.org/A005589>(k) to any starting value n always leads to 4 (cf. A016037 <http://oeis.org/A016037>, A133418 <http://oeis.org/A133418>). Has anyone (perhaps Diane Karloff, who is credited with this observation) written about this? Then maybe I could give the article to my daughter instead of having to write it myself. :-) My daughter and I learned about this fact from my son, who came home from camp last summer challenging us to make sense of baffling conversations like this: Son: Pick another number. Me: Okay, seventy-seven. Son: ... Seventy-seven is twelve, twelve is six, six is three, three is five, five is four, four is the magic number. Have any of you heard this “game” before? Jim Propp
I actually don’t find such sequences very interesting, but I know others do. In particular, my daughter has asked me to write a blog essay about the fact that
repeatedly applying the map k->A005589 <http://oeis.org/A005589>(k) to any starting value n always leads to 4 (cf. A016037 <http://oeis.org/A016037>, A133418 <http://oeis.org/A133418>).
Has anyone (perhaps Diane Karloff, who is credited with this observation) written about this? Then maybe I could give the article to my daughter instead of having to write it myself. :-)
Dunno about "written", though I'm sure it's mentioned in passing in lots of recreational maths books. One of those pop-maths YouTube channels did something about it a little while ago. ... Ah, found it: it's Matt Parker (standupmaths). https://youtube.com/watch?v=LYKn0UTIU4 -- g
A052363, Jim. You neglected "zero", so your candidate started differently from the version OEIS has chosen as canonical. In general, if you fail to find a sequence on OEIS, chopping off the first entry or two is always a good idea, because minor differences in definitions often lead to varying startup transients. Searching for 3,11,13,17,23 gives the sequence you were looking for as the first hit. Adding 73 makes it unique. Apparently this sequence was added 20 years ago by ... me! On Wed, Jun 3, 2020 at 11:13 AM Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
I actually don’t find such sequences very interesting, but I know others do. In particular, my daughter has asked me to write a blog essay about the fact that
repeatedly applying the map k->A005589 <http://oeis.org/A005589>(k) to any starting value n always leads to 4 (cf. A016037 <http://oeis.org/A016037 , A133418 <http://oeis.org/A133418>).
Has anyone (perhaps Diane Karloff, who is credited with this observation) written about this? Then maybe I could give the article to my daughter instead of having to write it myself. :-)
Dunno about "written", though I'm sure it's mentioned in passing in lots of recreational maths books. One of those pop-maths YouTube channels did something about it a little while ago. ... Ah, found it: it's Matt Parker (standupmaths). https://youtube.com/watch?v=LYKn0UTIU4
-- g
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I wrote something for my Mathematical Intelligencer column along these lines, except that for multiple-word number names I mapped to the *product* of the lengths of each individual word, not their sum. This means that 24 -> "twenty four" -> 6*4 = 24 is also a fixed point, as is 84,672. Huh, but I can't find it online everywhere. I think I only put my Intelligencer columns on the arxiv if they had some "real" math to them, and this was too flighty to qualify. Bizarrely, Futility Closet mentioned this last year: https://www.futilitycloset.com/2019/01/12/fortuitous-numbers/. Jim, I'll dig up a paper version for you, if you care. --Michael On Wed, Jun 3, 2020 at 11:53 AM Allan Wechsler <acwacw@gmail.com> wrote:
A052363, Jim. You neglected "zero", so your candidate started differently from the version OEIS has chosen as canonical.
In general, if you fail to find a sequence on OEIS, chopping off the first entry or two is always a good idea, because minor differences in definitions often lead to varying startup transients. Searching for 3,11,13,17,23 gives the sequence you were looking for as the first hit. Adding 73 makes it unique.
Apparently this sequence was added 20 years ago by ... me!
On Wed, Jun 3, 2020 at 11:13 AM Gareth McCaughan < gareth.mccaughan@pobox.com> wrote:
I actually don’t find such sequences very interesting, but I know others do. In particular, my daughter has asked me to write a blog essay about the fact that
repeatedly applying the map k->A005589 <http://oeis.org/A005589>(k) to any starting value n always leads to 4 (cf. A016037 < http://oeis.org/A016037 , A133418 <http://oeis.org/A133418>).
Has anyone (perhaps Diane Karloff, who is credited with this observation) written about this? Then maybe I could give the article to my daughter instead of having to write it myself. :-)
Dunno about "written", though I'm sure it's mentioned in passing in lots of recreational maths books. One of those pop-maths YouTube channels did something about it a little while ago. ... Ah, found it: it's Matt Parker (standupmaths). https://youtube.com/watch?v=LYKn0UTIU4
-- g
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-- Forewarned is worth an octopus in the bush.
Thanks, Michael, but no digging is necessary; I think the Matt Parker video (once I locate it) will provide exactly the level of information my 11-year-old seeks on the specific problem that raised her interest. Jim On Wed, Jun 3, 2020 at 12:18 PM Michael Kleber <michael.kleber@gmail.com> wrote:
I wrote something for my Mathematical Intelligencer column along these lines, except that for multiple-word number names I mapped to the *product* of the lengths of each individual word, not their sum. This means that 24 -> "twenty four" -> 6*4 = 24 is also a fixed point, as is 84,672.
Huh, but I can't find it online everywhere. I think I only put my Intelligencer columns on the arxiv if they had some "real" math to them, and this was too flighty to qualify. Bizarrely, Futility Closet mentioned this last year: https://www.futilitycloset.com/2019/01/12/fortuitous-numbers/. Jim, I'll dig up a paper version for you, if you care.
--Michael
On Wed, Jun 3, 2020 at 11:53 AM Allan Wechsler <acwacw@gmail.com> wrote:
A052363, Jim. You neglected "zero", so your candidate started differently from the version OEIS has chosen as canonical.
In general, if you fail to find a sequence on OEIS, chopping off the first entry or two is always a good idea, because minor differences in definitions often lead to varying startup transients. Searching for 3,11,13,17,23 gives the sequence you were looking for as the first hit. Adding 73 makes it unique.
Apparently this sequence was added 20 years ago by ... me!
On Wed, Jun 3, 2020 at 11:13 AM Gareth McCaughan < gareth.mccaughan@pobox.com> wrote:
I actually don’t find such sequences very interesting, but I know others do. In particular, my daughter has asked me to write a blog essay about the fact that
repeatedly applying the map k->A005589 <http://oeis.org/A005589 (k) to any starting value n always leads to 4 (cf. A016037 < http://oeis.org/A016037 , A133418 <http://oeis.org/A133418>).
Has anyone (perhaps Diane Karloff, who is credited with this observation) written about this? Then maybe I could give the article to my daughter instead of having to write it myself. :-)
Dunno about "written", though I'm sure it's mentioned in passing in lots of recreational maths books. One of those pop-maths YouTube channels did something about it a little while ago. ... Ah, found it: it's Matt Parker (standupmaths). https://youtube.com/watch?v=LYKn0UTIU4
-- g
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-- Forewarned is worth an octopus in the bush. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
AW: "A052363" < http://oeis.org/A052363 > I noticed that the sequence only has 40 terms. If one takes the (3..758) terms of A080777 [a(n), when spelled in English, is the smallest positive integer with exactly n letters] and removes 15, 24, 104, 115, 124, 1104, 1115, and 1124, I think that one gets 747 terms of A052363. http://oeis.org/A080777
"I think that one gets 747 terms of A052363." Sorry. Because the initial 1-4 also gets replaced by 0, it will only be 746 terms.
Offsetting errors. :) It is 747 after all: http://chesswanks.com/seq/b052363.txt
On Jun 3, 2020, at 3:16 PM, Hans Havermann <gladhobo@bell.net> wrote:
"I think that one gets 747 terms of A052363."
Sorry. Because the initial 1-4 also gets replaced by 0, it will only be 746 terms.
On Wed, Jun 3, 2020 at 11:13 AM Gareth McCaughan <gareth.mccaughan@pobox.com> wrote: Dunno about "written", though I'm sure it's mentioned in passing in
lots of recreational maths books. One of those pop-maths YouTube channels did something about it a little while ago. ... Ah, found it: it's Matt Parker (standupmaths). https://youtube.com/watch?v=LYKn0UTIU4
That link seems to be wrong. When I try it I get “Oops! Something went wrong.” Jim
On 03/06/2020 17:25, James Propp wrote:
On Wed, Jun 3, 2020 at 11:13 AM Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
Dunno about "written", though I'm sure it's mentioned in passing in
lots of recreational maths books. One of those pop-maths YouTube channels did something about it a little while ago. ... Ah, found it: it's Matt Parker (standupmaths). https://youtube.com/watch?v=LYKn0UTIU4
That link seems to be wrong. When I try it I get “Oops! Something went wrong.”
Zog, I must have mistranscribed it. (I use different computers for email and for watching YouTube. Never mind why.) Sorry. Ah, my problem was that I didn't mind Y. Try https://youtube.com/watch?v=LYKn0yUTIU4 instead. (I promise that I hadn't checked what the error was when I wrote "Never mind why". Just a happy coincidence.) -- g
participants (5)
-
Allan Wechsler -
Gareth McCaughan -
Hans Havermann -
James Propp -
Michael Kleber