[math-fun] Dupes in OEIS?
Is there supposed to be a difference between https://oeis.org/A206398 and https://oeis.org/A000793 ? (This came to my attention when I remembered a puzzle I invented as a kid: how many times a text might need to be typed on a typewriter with hammers re-soldered in a random order to get the desired result, given the number of the typewriter keys.) Thanks, Leo
On 2015-04-26 16:44, Leo Broukhis wrote:
Is there supposed to be a difference between https://oeis.org/A206398 and https://oeis.org/A000793 ?
Are you asking about the definitions? Or the contents? If the latter, then there's a 32760 in A000793 instead of a 30030 in the same position in A206398. If you believe the sequences *should* be identical, based on their definitions, then you may be able to figure out which one is mistaken at the positions they disagree in. I think two sequences with identical elements are considered distinct unless you can prove that the two series should be identical.
(This came to my attention when I remembered a puzzle I invented as a kid: how many times a text might need to be typed on a typewriter with hammers re-soldered in a random order to get the desired result, given the number of the typewriter keys.)
Thanks, Leo
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The definitions seem equivalent to me ("largest LCM of partitions of n" vs "Maximum least common multiple of some set of positive integers adding up to n"), therefore whenever A000793 and A206398 diverge, the largest value (in A000793) wins. I think that A206398 should be scrapped. Leo On Sun, Apr 26, 2015 at 5:27 PM, Michael Greenwald <mbgreen@seas.upenn.edu> wrote:
On 2015-04-26 16:44, Leo Broukhis wrote:
Is there supposed to be a difference between https://oeis.org/A206398 and https://oeis.org/A000793 ?
Are you asking about the definitions? Or the contents?
If the latter, then there's a 32760 in A000793 instead of a 30030 in the same position in A206398. If you believe the sequences *should* be identical, based on their definitions, then you may be able to figure out which one is mistaken at the positions they disagree in.
I think two sequences with identical elements are considered distinct unless you can prove that the two series should be identical.
(This came to my attention when I remembered a puzzle I invented as a kid: how many times a text might need to be typed on a typewriter with hammers re-soldered in a random order to get the desired result, given the number of the typewriter keys.)
Thanks, Leo
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the differences in the entries upto n=47 are: n=29, 2520, 2310, LCM {9, 8, 7, 5} is 2520 n=40, 27720, 20020, LCM {11, 9, 8, 7, 5} is 27720 n=42, 32760, 30030, LCM {13, 9, 8, 7, 5} is 32760 so it looks like the PARI program in A206398 misses multiples of 9*8*7*5. Any PARIsians on this list? Wouter. -----Original Message----- From: Leo Broukhis Sent: Monday, April 27, 2015 3:06 AM To: greenwald@cis.upenn.edu Cc: math-fun Subject: Re: [math-fun] Dupes in OEIS? The definitions seem equivalent to me ("largest LCM of partitions of n" vs "Maximum least common multiple of some set of positive integers adding up to n"), therefore whenever A000793 and A206398 diverge, the largest value (in A000793) wins. I think that A206398 should be scrapped. Leo On Sun, Apr 26, 2015 at 5:27 PM, Michael Greenwald <mbgreen@seas.upenn.edu> wrote:
On 2015-04-26 16:44, Leo Broukhis wrote:
Is there supposed to be a difference between https://oeis.org/A206398 and https://oeis.org/A000793 ?
Are you asking about the definitions? Or the contents?
If the latter, then there's a 32760 in A000793 instead of a 30030 in the same position in A206398. If you believe the sequences *should* be identical, based on their definitions, then you may be able to figure out which one is mistaken at the positions they disagree in.
I think two sequences with identical elements are considered distinct unless you can prove that the two series should be identical.
(This came to my attention when I remembered a puzzle I invented as a kid: how many times a text might need to be typed on a typewriter with hammers re-soldered in a random order to get the desired result, given the number of the typewriter keys.)
Thanks, Leo
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Good catch Leo and Wouter. My sequence A206398 is incorrect (and the program, as written, is unsalvageable). To use n = 29 as an example: It correctly considers the possibility that, say, 9 is a member of the set, but incorrectly assumes that the associated value is lcm(a(29 - 9), 9) = lcm(420, 9) = 1260 and rejects this since 1260 < 2310 = lcm(a(28), 1). I'll take care of the OEIS entry. Charles Greathouse Analyst/Programmer Case Western Reserve University On Mon, Apr 27, 2015 at 5:11 AM, Wouter Meeussen <wouter.meeussen@telenet.be
wrote:
the differences in the entries upto n=47 are:
n=29, 2520, 2310, LCM {9, 8, 7, 5} is 2520 n=40, 27720, 20020, LCM {11, 9, 8, 7, 5} is 27720 n=42, 32760, 30030, LCM {13, 9, 8, 7, 5} is 32760
so it looks like the PARI program in A206398 misses multiples of 9*8*7*5. Any PARIsians on this list?
Wouter.
-----Original Message----- From: Leo Broukhis Sent: Monday, April 27, 2015 3:06 AM To: greenwald@cis.upenn.edu Cc: math-fun Subject: Re: [math-fun] Dupes in OEIS? The definitions seem equivalent to me ("largest LCM of partitions of n" vs "Maximum least common multiple of some set of positive integers adding up to n"), therefore whenever A000793 and A206398 diverge, the largest value (in A000793) wins. I think that A206398 should be scrapped.
Leo
On Sun, Apr 26, 2015 at 5:27 PM, Michael Greenwald <mbgreen@seas.upenn.edu> wrote:
On 2015-04-26 16:44, Leo Broukhis wrote:
Is there supposed to be a difference between https://oeis.org/A206398 and https://oeis.org/A000793 ?
Are you asking about the definitions? Or the contents?
If the latter, then there's a 32760 in A000793 instead of a 30030 in the same position in A206398. If you believe the sequences *should* be identical, based on their definitions, then you may be able to figure out which one is mistaken at the positions they disagree in.
I think two sequences with identical elements are considered distinct unless you can prove that the two series should be identical.
(This came to my attention when I remembered a puzzle I invented as a kid: how many times a text might need to be typed on a typewriter with hammers re-soldered in a random order to get the desired result, given the number of the typewriter keys.)
Thanks, Leo
_______________________________________________ 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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In this session: ----- In[1]:= f[n_] := If[n==1, 1, LCM[n,f[n-1]] ] In[2]:= f[11] Out[3]= 27720 In[4]:= g[n_] := f[n]^(1/n) In[5]:= g[11] 3/11 2/11 1/11 Out[5]= 2 3 385 In[6]:= h[n] := N[g[n], 10] In[7]:= h[11] Out[7]= h[11] In[8]:= N[g[11], 10] Out[8]= 2.534488315 ----- Why does In[7] fail to get the same output as In[8] ??? Is there no way to create a function that does the same thing as In[8] (for n in place of 11) ??? The idea was to show that lim LCM[1,...,n]^(1/n) = e n->oo None of my attempts to get g[n] to approach a numerical limit in Mma were successful. In fact, it gets seriously confused when I ask for N[g[10000]] Thanks, Dan
Need h[n_], not h[n]. --Michael On Mon, Apr 27, 2015 at 3:44 PM, Dan Asimov <dasimov@earthlink.net> wrote:
In this session:
----- In[1]:= f[n_] := If[n==1, 1, LCM[n,f[n-1]] ]
In[2]:= f[11]
Out[3]= 27720
In[4]:= g[n_] := f[n]^(1/n)
In[5]:= g[11]
3/11 2/11 1/11 Out[5]= 2 3 385
In[6]:= h[n] := N[g[n], 10]
In[7]:= h[11]
Out[7]= h[11]
In[8]:= N[g[11], 10]
Out[8]= 2.534488315 -----
Why does In[7] fail to get the same output as In[8] ???
Is there no way to create a function that does the same thing as In[8] (for n in place of 11) ???
The idea was to show that
lim LCM[1,...,n]^(1/n) = e n->oo
None of my attempts to get g[n] to approach a numerical limit in Mma were successful.
In fact, it gets seriously confused when I ask for N[g[10000]]
Thanks,
Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.
Thanks. Aargh, total beginner's mistake. Okay, got that working fine. But is there any way I can get it to try to find lim h[n] n->oo without its giving an error message or crashing badly? For example, this command: In[1729]:= Limit[h[n], n -> Infinity] gets a segmentation fault, and kills the Mma program. --Dan
On Apr 27, 2015, at 12:53 PM, Michael Kleber <michael.kleber@gmail.com> wrote:
Need h[n_], not h[n].
--Michael
On Mon, Apr 27, 2015 at 3:44 PM, Dan Asimov <dasimov@earthlink.net> wrote:
In this session:
----- In[1]:= f[n_] := If[n==1, 1, LCM[n,f[n-1]] ]
In[2]:= f[11]
Out[3]= 27720
In[4]:= g[n_] := f[n]^(1/n)
In[5]:= g[11]
3/11 2/11 1/11 Out[5]= 2 3 385
In[6]:= h[n] := N[g[n], 10]
In[7]:= h[11]
Out[7]= h[11]
In[8]:= N[g[11], 10]
Out[8]= 2.534488315 -----
Why does In[7] fail to get the same output as In[8] ???
Is there no way to create a function that does the same thing as In[8] (for n in place of 11) ???
The idea was to show that
lim LCM[1,...,n]^(1/n) = e n->oo
None of my attempts to get g[n] to approach a numerical limit in Mma were successful.
In fact, it gets seriously confused when I ask for N[g[10000]]
Thanks,
Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- 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
On 2015-04-27 12:44, Dan Asimov wrote:
In this session:
----- In[1]:= f[n_] := If[n==1, 1, LCM[n,f[n-1]] ]
In[2]:= f[11]
Out[3]= 27720
Shorter: In[131]:= FoldList[LCM, 1, Range[19]] Out[131]= {1, 1, 2, 6, 12, 60, 60, 420, 840, 2520, 2520, 27720, 27720, 360360, 360360, 360360, 720720, 12252240, 12252240, 232792560} --rwg
participants (7)
-
Charles Greathouse -
Dan Asimov -
Leo Broukhis -
Michael Greenwald -
Michael Kleber -
rwg -
Wouter Meeussen