[seqfan] Proposal for "Big Numbers" paper

[David Wilson]

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).