Re: [math-fun] Numbers Aplenty
Jim, You might have more success posting your question to the SeqFan mailing list. You can join at http://list.seqfan.eu/cgi-bin/mailman/listinfo/seqfan. There sequence fans over there that may jump at your challenge. --Edwin On Mon, Jan 6, 2014 at 12:08 AM, James Propp <jamespropp@gmail.com> wrote:
I didn't know about Sloane's gap. Very interesting!
I was wrong: the first number that is less common in the OEIS than its successor is 14, not 11.
I don't know what the situation is if one restricts to increasing sequences; can anyone look into this?
Jim Propp
On Sunday, January 5, 2014, David Makin wrote:
Not sure about sorting all numbers in terms of interest - but clearly the *most* interesting have to be 0 and 1 ;)
On 5 Jan 2014, at 23:07, W. Edwin Clark wrote:
A place to start with such investigations is perhaps the famous paper on "Sloane's gap" ( http://arxiv.org/pdf/1101.4470.pdf ) which discusses the distribution of N(n) = the number of occurrences of n in the OEIS.
On Sun, Jan 5, 2014 at 5:46 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
What is the smallest value of n such that n+1 appears in more of the increasing sequences in the OEIS than n does?
The reason I want to restrict attention to increasing sequences in the OEIS is that these correspond to interesting subsets of the positive integers. I suppose if anyone wants to answer my question with the word "increasing" omitted, I'd be interested in that too. Conjecture: The n that you get is the same for both versions of my question. Refined conjecture: in both cases, n is 11.
Jim Propp
Good idea! But before I join seqfans and post my question, I'd like to make sure that the question hasn't already been posed and answered there. I went to the seqfans site, but didn't see anything like an FAQ or a comprehensive index of subject-lines. Are any math-funsters also seqfans, and if so, can anyone comment on whether my question is a new one? (Seems unlikely to me, the more I think about it.) Jim Propp On Mon, Jan 6, 2014 at 12:19 AM, W. Edwin Clark <wclark@mail.usf.edu> wrote:
Jim,
You might have more success posting your question to the SeqFan mailing list. You can join at http://list.seqfan.eu/cgi-bin/mailman/listinfo/seqfan. There sequence fans over there that may jump at your challenge.
--Edwin
On Mon, Jan 6, 2014 at 12:08 AM, James Propp <jamespropp@gmail.com> wrote:
I didn't know about Sloane's gap. Very interesting!
I was wrong: the first number that is less common in the OEIS than its successor is 14, not 11.
I don't know what the situation is if one restricts to increasing sequences; can anyone look into this?
Jim Propp
On Sunday, January 5, 2014, David Makin wrote:
Not sure about sorting all numbers in terms of interest - but clearly the *most* interesting have to be 0 and 1 ;)
On 5 Jan 2014, at 23:07, W. Edwin Clark wrote:
A place to start with such investigations is perhaps the famous paper on "Sloane's gap" ( http://arxiv.org/pdf/1101.4470.pdf ) which discusses the distribution of N(n) = the number of occurrences of n in the OEIS.
On Sun, Jan 5, 2014 at 5:46 PM, James Propp <jamespropp@gmail.com <javascript:;>> wrote:
What is the smallest value of n such that n+1 appears in more of the increasing sequences in the OEIS than n does?
The reason I want to restrict attention to increasing sequences in the OEIS is that these correspond to interesting subsets of the positive integers. I suppose if anyone wants to answer my question with the word "increasing" omitted, I'd be interested in that too. Conjecture: The n that you get is the same for both versions of my question. Refined conjecture: in both cases, n is 11.
Jim Propp
math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Dear James, Your question is not exactly a new one but - the database is constantly evolving - the restriction to monotonous sequences is important and requires preprocessing and the article about Sloane's Gap by Delahaye and al. is full of misinterpretations and unwarranted hypothesis. No need to subscribe to seqfan if you are not interested daily in integer sequences. I will ask the question myself on your behalf and report on this on math-fun. Olivier Gérard seqfan Mailing List administrator
Well, I couldn't resist doing it myself. Here are two graphics, based on the latest version of the database (January 4th 2014): http://list.seqfan.eu/seqfans/olivier/OEIS_Frequencies_A.jpg http://list.seqfan.eu/seqfans/olivier/OEIS_Frequencies_B.jpg The horizontal scale is the integer under consideration The vertical scale is logarithmic in base 10. It counts number of apparitions in the OEIS sequences. The upper curve is total apparitions in the stripped down version (the first 3 lines for each sequence when available.) The middle curve is the same for increasing sequences (after removing signs) The lower curve is the same for strictly increasing sequences (after removing signs) Olivier Raw data (from 0 to 100, y-coordinates of each curve): {{601621,39420,13687},{864198,117890,55500},{464087,50809,31725},{341000,42130,25098},{292704,36359,20578},{243521,33965,20092},{223598,30092,17380},{198621,28804,17858},{191759,25350,14853},{171932,23733,14187},{77475,20979,13224},{70794,22058,14699},{70521,19816,12692},{58798,19718,13050},{48073,15613,10211},{50902,16975,11024},{57752,17835,11269},{44147,17014,11693},{41275,14398,9725},{40192,16026,11314},{40556,14397,9964},{38703,14910,10197},{31788,12802,9084},{33746,14622,10787},{39539,14637,10189},{31437,13032,9357},{26774,11439,8286},{28370,12048,8735},{29996,11682,8661},{28940,13096,10100},{31545,12379,9124},{29626,13533,10443},{30311,11897,8589},{22845,10681,8225},{22619,10102,7641},{23732,10061,7835},{30560,11975,9217},{24972,12199,9825},{18603,8907,7088},{18721,9171,7316},{23604,10145,8057},{22989,11521,9434},{23154,9831,7836},{21326,10980,9127},{18837,8743,7162},{20340,9509,7681},{17241,8266,6799},{19696,10484,8727},{22422,9613,7842},{18847,9347,7692},{17662,8678,7324},{15732,8254,7039},{16529,8056,6771},{18441,9965,8542},{17221,8375,7069},{18464,8941,7527},{19625,8821,7431},{15242,8127,6906},{14527,7539,6436},{16641,9429,8261},{20172,9059,7666},{17459,9762,8567},{13673,7340,6362},{15871,8210,7083},{21238,9553,7732},{14275,7933,6876},{14530,7938,6959},{14968,9159,8135},{11905,7050,6246},{11644,7132,6343},{14028,7563,6678},{15146,9167,8168},{15900,8288,7204},{14636,9190,8283},{10121,6669,5977},{10997,7052,6280},{10732,6799,6121},{11025,7001,6273},{10898,6812,6123},{12531,8431,7655},{12694,7434,6596},{13401,7872,6868},{9218,6284,5687},{11686,8074,7409},{12596,7091,6263},{10180,6773,5981},{8514,5981,5435},{8658,6140,5552},{9798,6365,5705},{12748,8358,7330},{11717,6961,6182},{10454,6804,6022},{8269,5565,5069},{8219,5802,5259},{7812,5609,5075},{8076,5604,5149},{11367,6491,5757},{11145,7738,6990},{7880,5431,4948},{9100,6017,5413},{11002,6892,6133}}
Olivier, Sorry, what's the difference between A and B? Jim On Monday, January 6, 2014, Olivier Gerard wrote:
Well,
I couldn't resist doing it myself.
Here are two graphics, based on the latest version of the database (January 4th 2014):
http://list.seqfan.eu/seqfans/olivier/OEIS_Frequencies_A.jpg
http://list.seqfan.eu/seqfans/olivier/OEIS_Frequencies_B.jpg
The horizontal scale is the integer under consideration The vertical scale is logarithmic in base 10. It counts number of apparitions in the OEIS sequences. The upper curve is total apparitions in the stripped down version (the first 3 lines for each sequence when available.) The middle curve is the same for increasing sequences (after removing signs) The lower curve is the same for strictly increasing sequences (after removing signs)
Olivier
Raw data (from 0 to 100, y-coordinates of each curve):
{{601621,39420,13687},{864198,117890,55500},{464087,50809,31725},{341000,42130,25098},{292704,36359,20578},{243521,33965,20092},{223598,30092,17380},{198621,28804,17858},{191759,25350,14853},{171932,23733,14187},{77475,20979,13224},{70794,22058,14699},{70521,19816,12692},{58798,19718,13050},{48073,15613,10211},{50902,16975,11024},{57752,17835,11269},{44147,17014,11693},{41275,14398,9725},{40192,16026,11314},{40556,14397,9964},{38703,14910,10197},{31788,12802,9084},{33746,14622,10787},{39539,14637,10189},{31437,13032,9357},{26774,11439,8286},{28370,12048,8735},{29996,11682,8661},{28940,13096,10100},{31545,12379,9124},{29626,13533,10443},{30311,11897,8589},{22845,10681,8225},{22619,10102,7641},{23732,10061,7835},{30560,11975,9217},{24972,12199,9825},{18603,8907,7088},{18721,9171,7316},{23604,10145,8057},{22989,11521,9434},{23154,9831,7836},{21326,10980,9127},{18837,8743,7162},{20340,9509,7681},{17241,8266,6799},{19696,10484,8727},{22422,9613,7842},{18847,9347,7692},{17662,8678,7324},{15732,8254,7039},{16529,8056,6771},{18441,9965,8542},{17221,8375,7069},{18464,8941,7527},{19625,8821,7431},{15242,8127,6906},{14527,7539,6436},{16641,9429,8261},{20172,9059,7666},{17459,9762,8567},{13673,7340,6362},{15871,8210,7083},{21238,9553,7732},{14275,7933,6876},{14530,7938,6959},{14968,9159,8135},{11905,7050,6246},{11644,7132,6343},{14028,7563,6678},{15146,9167,8168},{15900,8288,7204},{14636,9190,8283},{10121,6669,5977},{10997,7052,6280},{10732,6799,6121},{11025,7001,6273},{10898,6812,6123},{12531,8431,7655},{12694,7434,6596},{13401,7872,6868},{9218,6284,5687},{11686,8074,7409},{12596,7091,6263},{10180,6773,5981},{8514,5981,5435},{8658,6140,5552},{9798,6365,5705},{12748,8358,7330},{11717,6961,6182},{10454,6804,6022},{8269,5565,5069},{8219,5802,5259},{7812,5609,5075},{8076,5604,5149},{11367,6491,5757},{11145,7738,6990},{7880,5431,4948},{9100,6017,5413},{11002,6892,6133}} _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
-
James Propp -
Olivier Gerard -
W. Edwin Clark