[seqfan] Re: Proposal for "Big Numbers" paper
David Wilson
davidwwilson at comcast.net
Mon Feb 10 01:25:24 CET 2014
I'm surprised that A007698 & A007699 are not mentioned in this index entry.
At any rate, could someone compute A007698(1403) and A007699(1403) for me?
From: Neil Sloane [mailto:njasloane at gmail.com]
Sent: Wednesday, January 29, 2014 5:14 PM
To: Sequence Fanatics Discussion list
Cc: David Wilson
Subject: Re: [seqfan] Proposal for "Big Numbers" paper
Don't forget the Index to the OEIS where there
is a section on
sequences which agree for a long time but are different, sequences related
to :
I didn't check if the ones
you mention are there - if they aren't, please add them!
Best regards
Neil
On Wed, Jan 29, 2014 at 12:55 PM, Antti Karttunen
<antti.karttunen at gmail.com> wrote:
Also, how about large _exact_ and _known_ values of n such that two
sequences (defined in a reasonably simply manner) do not diverge until
at that point?
For example, http://oeis.org/A235921
"Numbers n such that smallest number not dividing n^2 (A236454) is
different from smallest prime not dividing n (A053669)"
does not differ from A236432, "a(n) = (2n-1)*210; numbers which are
210 times an odd number"
until at n = 1062348, where the former has A235921(1062348) =
446185740, while the latter has A236432(1062348) = 446185950 with all
preceding terms equal.
As when these two sequences:
http://oeis.org/A079599
http://oeis.org/A126002
differ for the first time, I don't exactly know. (And also, the
encoding systems employed might be not so intuitive for the general
populace).
Any other good examples?
Yours,
Antti
On Sat, Jan 25, 2014 at 4:54 AM, <seqfan-request at list.seqfan.eu> wrote:
> From: "David Wilson" <davidwwilson at comcast.net>
> To: "'Sequence Fanatics Discussion list'" <seqfan at list.seqfan.eu>
> Subject: [seqfan] Proposal for "Big Numbers" paper
> Message-ID: <000c01cf1977$d2fc81c0$78f58540$@comcast.net>
> Content-Type: text/plain; charset="us-ascii"
>
> 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) =
> 80658175170943878571660636856403766975289505440883277824000000000000
> 52! = number of ways to shuffle a deck of cards (without jokers).
>
> A011557(100) =
>
1000000000000000000000000000000000000000000000000000000000000000000000000000
> 0000000000000000000000000
> 10^100, a googol.
>
> A114440(15095) =
>
1084464230395358729932151438017082487888975184391965518658152244719602291501
>
3498755182422783168249743964253744721999890517357463607557093872677041563756
>
6547495970738297545359694233469258248066044412311789418336202690430748419494
>
3533374289213175436767660095097341776774737704214452219362042142821400148498
>
6836733868054994984612164832174339221137837017699883320992120665521746473983
>
1625543921041252648766408996885700710913879052486492812317563281491911243925
>
4273788773691427686404063230668247974721311479671409775684127892567107590504
>
0965622203570652239329167789023141169583945522024583639602764844086144054334
>
4125146667943578032458072195974008992176685068654594958348314899096787905903
>
2692273036724661022533504520746569434366728325919336695072199658573011889440
>
2624162399404426144503547718692814107138420936301106286615600332822535921841
>
7581786664993612723261535530033504534359456197194706824538502279255382972206
>
0345252788143549518083651562951378522396595828064708693825881694616491563006
>
9310420816697268900748652903486008347345997664784377902556126668240992674343
>
6435548435186073490637074087381530918243621501901195914047236424084375593247
>
2279709586011392723417973955501965899300525729773575625483069870019644473846
>
7685891758469219474040310330071977656807191063602031108704555558860664475868
>
4325277244510326965842198914723217408000000000000000000000000000000000000000
> 000000000000000000000000000000000000000000000000000000000000000000
> Largest number which, when repeatedly divided by the sum of its digits,
> eventually reaches 1 (after 440 iterations).
>
>
>
> ------------------------------
>
> Message: 11
> Date: Fri, 24 Jan 2014 21:54:31 -0500 (EST)
> From: franktaw at netscape.net
> To: seqfan at list.seqfan.eu
> Subject: [seqfan] Re: Proposal for "Big Numbers" paper
> Message-ID: <8D0E78FE7FB0B76-178C-CF19 at webmail-d215.sysops.aol.com>
> Content-Type: text/plain; charset="us-ascii"; format=flowed
>
> 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) =
> 80658175170943878571660636856403766975289505440883277824000000000000
> 52! = number of ways to shuffle a deck of cards (without jokers).
>
> A011557(100) =
> 1000000000000000000000000000000000000000000000000000000000000000000000000
> 000
> 0000000000000000000000000
> 10^100, a googol.
>
> A114440(15095) =
> 1084464230395358729932151438017082487888975184391965518658152244719602291
> 501
> 3498755182422783168249743964253744721999890517357463607557093872677041563
> 756
> 6547495970738297545359694233469258248066044412311789418336202690430748419
> 494
> 3533374289213175436767660095097341776774737704214452219362042142821400148
> 498
> 6836733868054994984612164832174339221137837017699883320992120665521746473
> 983
> 1625543921041252648766408996885700710913879052486492812317563281491911243
> 925
> 4273788773691427686404063230668247974721311479671409775684127892567107590
> 504
> 0965622203570652239329167789023141169583945522024583639602764844086144054
> 334
> 4125146667943578032458072195974008992176685068654594958348314899096787905
> 903
> 2692273036724661022533504520746569434366728325919336695072199658573011889
> 440
> 2624162399404426144503547718692814107138420936301106286615600332822535921
> 841
> 7581786664993612723261535530033504534359456197194706824538502279255382972
> 206
> 0345252788143549518083651562951378522396595828064708693825881694616491563
> 006
> 9310420816697268900748652903486008347345997664784377902556126668240992674
> 343
> 6435548435186073490637074087381530918243621501901195914047236424084375593
> 247
> 2279709586011392723417973955501965899300525729773575625483069870019644473
> 846
> 7685891758469219474040310330071977656807191063602031108704555558860664475
> 868
> 4325277244510326965842198914723217408000000000000000000000000000000000000
> 000
> 000000000000000000000000000000000000000000000000000000000000000000
> Largest number which, when repeatedly divided by the sum of its digits,
> eventually reaches 1 (after 440 iterations).
>
>
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>
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--
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.
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