an On-Line EIS Hall of Fame
Robert G. Wilson v
rgwv at kspaint.com
Tue Oct 23 22:16:48 CEST 2001
Sequence Fanatics,
I would like to propose an Integer Sequence Hall of Fame. Each
sequence nominated would have a short essay explaining why it should be
included. This would be much akin to Neil J. A. Sloane, “My favorite
integer sequences,” in Sequences and their Applications (Proceedings of
SETA '98) but current and broadly based.
As an example, let me start with A006345, “The Linus sequence: a(n)
avoids longest repetition.” My reason is simply to acknowledge the spark
of intuition of its author to read a comic strip and from there proceed
to a sequence. What I would not like to see are the common sequences
such as the Bell numbers or the Fibonacci sequence. These sequences have
their own venue. Rather a sequence A003681 “a(n) = min ( p +- q > 1 : pq
= Product a(k), k = 1.. n-1)” probably has no sociably redeeming virtue
but it has no precedent. Many can imitate but few can create an
original. And not all originals are worthy of honor. Out of the 2^16
plus sequences, only about 75 of them should be so honored. Out of the
hundreds plus Beatty sequences, can we identify the first? I'm guessing
it is A000201 “floor(n*tau).” Those are the some of the sequences I am
looking for inclusion in the On-Line Encyclopedia of Integer Sequences
Hall of Fame.
Who would judge these candidates? I believe that the fifty plus of
us who are regular contributors can do this via this forum. I suggest
each of us nominate just ten sequences, not of your own making, and post
them to this list. I suspect that by popular choose we will see that
about 75 sequences emerge.
That being the case, let me jump in first with the following
sequences:
A000201 A Samuel Beatty sequence: floor(n*tau).
A002859 Ulam’s sequence: a(1)=1, a(2)=3; for n>=3, a(n) is smallest
number which is uniquely of the form a(j)+a(k), with
1<=j<k<n.
A003022 Golomb Ruler: Shortest ruler with n marks.
A003681 a(n) = min ( p +- q > 1 : pq = Product a(k), k = 1.. n-1).
A004018 Theta series of square lattice (or number of ways of writing n
as
a sum of 2 squares).
A005105 Class 1+ primes.
A005235 Fortunate Primes: : let q_n be least prime > x_n = 1 + product
prime_i, i=1..n; sequence gives a(n) = q_n-x_n+1.
A006345 The Linus sequence: a(n) avoids longest repetition.
A007448 Knuth’s sequence: a(n+1) = 1 + min ( 2 a[ n/2 ],3 a[ n/3 ] ).
A047713 Euler-Jacobi pseudoprimes: 2^{(n-1)/2} == (2 / n) mod n.
Gratefully submitted,
Robert G. "Bob" Wilson, V
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