[seqfan] Re: Proposal for "Big Numbers" paper

Sat Jan 25 19:59:25 CET 2014

Indeed, it is possible to come up with mind-bogglingly large numbers like
Graham's number, or Ackermann numbers, or 10^(10^23), but I was hoping for
something more along the lines of:

- The number can be found as an OEIS element, ergo can be written out in
decimal. I think a large decimal number is more impressive than a succinct
expression like 10^(10^23).

- Numbers which is familiar or graspable (with a modicum of explanation) by
a non-mathematician. For example, people are familiar with the notion of a
googol = 10^100, while 52! can be explained as the number of ways to shuffle
a deck of cards.

- Numbers that might be used to discuss mathematical concepts. For example,
to explain the significance of 4700063497 (the smallest number > 1 such that
2^n == 3 (mod n)), motivates a discussion of modular arithmetic and perhaps
multiplicative groups.

- I would favor numbers which are "unexpectedly" large. We might expect 2^n
(mod n) == 3 for some small n, but in fact we have to wait until n =
4700063497.

- The less "arbitrary" a number is, the better. I'm less impressed with
A124505(27) = 10827543712227210782977570287648768000000 (the number of
regular 27-dimensional simplices that can be inscribed in the 27-dimensional
cube), because it seems like an arbitrarily chosen element in a fast-growing
sequence.

I'm open to other people's ideas.

Also, if the whole idea of an "OEIS big number" submission to Numberphile
seems off the wall, please tell me and I'll go away.

> > the vertices of a 27-cube.

> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Neil
> Sloane
> Sent: Saturday, January 25, 2014 1:14 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: Proposal for "Big Numbers" paper
> 
> Then there is Gijswijt's sequence A090822, which starts off with 1's, 2's,
3's
> and 4's. You could search until the universe went cold before finding a 5.
But
> the sequence goes to infinity, with the first 5 at term (about)
10^(10^23).
> 
> 
> On Fri, Jan 24, 2014 at 10:37 PM, Andrew Weimholt
> <andrew.weimholt at gmail.com
> > wrote:
> 
> > A124505(27) = 10827543712227210782977570287648768000000
> > Number of regular 27-dimensional simplices that can be inscribed on
> > the vertices of a 27-cube.
> >
> > Andrew
> >
> >
> > On Fri, Jan 24, 2014 at 6:54 PM, <franktaw at netscape.net> wrote:
> >
> > > A121977(1) = 100000000011111112222222333333444445555666778
> > > Smallest number such that each digit 0-9 occurs a different number
> > > of times.
> > >
> > > Franklin T. Adams-Watters
> > >
> > >
> > > -----Original Message-----
> > > From: David Wilson <davidwwilson at comcast.net>
> > > To: 'Sequence Fanatics Discussion list' <seqfan at list.seqfan.eu>
> > > Sent: Fri, Jan 24, 2014 8:47 pm
> > > Subject: [seqfan] Proposal for "Big Numbers" paper
> > >
> > >
> > > I was watching some of the Numberphile videos on Youtube, and partly
> > > motivated by the recent foray into Harshad numbers, I had the
> > > following thought. It might be nice for the seqfans to write a
> > > collective paper
> > (OEIS
> > > editors et al) on interesting large numbers in the OEIS, which we
> > > could then submit to the Numberphile people as a possible subject
> > > for a video or videos. (Face it, who are more Numberphilic than the
> > > seqfans?)
> > >
> > > Optimally, we would want to choose large numbers with fundamental
> > > appeal, that could reasonably be explained in a video. I give the
> > > examples at the end. The paper could also include some discussion of
> > > the meaning of the number.
> > >
> > > A045911(6195) = 78526384
> > > Almost certainly the largest number which is neither a positive
> > > cube, nor the sum of a positive cube and a prime number.
> > >
> > > A035490(54) = 252992198
> > > The number of perfect in-shuffles of increasing size required to
> > > bring
> > the
> > > 54th card to the top of an infinite deck.
> > >
> > > A036236(3) = 4700063497
> > > Smallest number n > 1 such that 2^n == 3 (mod n).
> > >
> > > A003001(11) = 277777788888899
> > > Smallest number of persistence 11 (product of digits can be taken 11
> > times
> > > before reaching a single-digit number). No number is believed to
> > > have persistence 12 or more.
> > >
> > > A075152(3) = 43252003274489856000
> > > Number of permutations of a 3x3x3 Rubik's cube (already subject of a
> > > Numberphile video).
> > >
> > > A009190(2) = 2061519317176132799110061 Smallest known twin peak. N
> > > and N+146 have smallest prime factor 73, all numbers between them
> > > have a prime factor < 73.
> > >
> > > A001228(26) =
> 808017424794512875886459904961710757005754368000000000
> > > Order of the largest sporadic simple group, the Monster group.
> > >
> > > A000142(52) =
> > >
> 8065817517094387857166063685640376697528950544088327782400000000000
> 0
> > > 52! = number of ways to shuffle a deck of cards (without jokers).
> > >
> > > A011557(100) =
> > >
> 1000000000000000000000000000000000000000000000000000000000000000000
> 0
> > > 00000
> > > 000
> > > 0000000000000000000000000
> > > 10^100, a googol.
> > >
> > > A114440(15095) =
> > >
> 1084464230395358729932151438017082487888975184391965518658152244719
> 6
> > > 02291
> > > 501
> > >
> 3498755182422783168249743964253744721999890517357463607557093872677
> 0
> > > 41563
> > > 756
> > >
> 6547495970738297545359694233469258248066044412311789418336202690430
> 7
> > > 48419
> > > 494
> > >
> 3533374289213175436767660095097341776774737704214452219362042142821
> 4
> > > 00148
> > > 498
> > >
> 6836733868054994984612164832174339221137837017699883320992120665521
> 7
> > > 46473
> > > 983
> > >
> 1625543921041252648766408996885700710913879052486492812317563281491
> 9
> > > 11243
> > > 925
> > >
> 4273788773691427686404063230668247974721311479671409775684127892567
> 1
> > > 07590
> > > 504
> > >
> 0965622203570652239329167789023141169583945522024583639602764844086
> 1
> > > 44054
> > > 334
> > >
> 4125146667943578032458072195974008992176685068654594958348314899096
> 7
> > > 87905
> > > 903
> > >
> 2692273036724661022533504520746569434366728325919336695072199658573
> 0
> > > 11889
> > > 440
> > >
> 2624162399404426144503547718692814107138420936301106286615600332822
> 5
> > > 35921
> > > 841
> > >
> 7581786664993612723261535530033504534359456197194706824538502279255
> 3
> > > 82972
> > > 206
> > >
> 0345252788143549518083651562951378522396595828064708693825881694616
> 4
> > > 91563
> > > 006
> > >
> 9310420816697268900748652903486008347345997664784377902556126668240
> 9
> > > 92674
> > > 343
> > >
> 6435548435186073490637074087381530918243621501901195914047236424084
> 3
> > > 75593
> > > 247
> > >
> 2279709586011392723417973955501965899300525729773575625483069870019
> 6
> > > 44473
> > > 846
> > >
> 7685891758469219474040310330071977656807191063602031108704555558860
> 6
> > > 64475
> > > 868
> > >
> 4325277244510326965842198914723217408000000000000000000000000000000
> 0
> > > 00000
> > > 000
> > >
> 000000000000000000000000000000000000000000000000000000000000000000
> > > Largest number which, when repeatedly divided by the sum of its
> > > digits, eventually reaches 1 (after 440 iterations).
> > >
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> > >
> > > _______________________________________________
> > >
> > > Seqfan Mailing list - http://list.seqfan.eu/
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
> 
> 
> 
> --
> Dear Friends, I have now retired from AT&T. New coordinates:
> 
> 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 at gmail.com
> 
> _______________________________________________
> 
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