[seqfan] Interim database of my new sequence related work, and index of existing material

Robert Munafo mrob27 at gmail.com
Wed Dec 30 20:02:07 CET 2009

I've been sitting on dozens of new sequences and revisions to existing
sequences, and an doing new work on an ongoing basis, and it has gotten to
the point where I need to be able to do searches and have the search results
include my own work.

Since we're only just barely into week 2 of the moratorium on updating the
server, I have begun a file that augments the main OEIS, to organize and
hold this work so I don't have to strain my memory trying to format the
edits and submissions once such action are once again appropriate.

The moratorium came at a bad time for me, inasmuch as NJAS had just
encouraged us all to overcome our doubts and submit anything we think is
interesting. I had just started submitting material written in the margins
of my copy of NJAS's 1971 book when the "do not submit" request came out.

I am using A-numbers from the dispenser (including A171871 --- A171897,
which I *hereby reserve until further notice*, even if that is more than a

The data, in eisBTfry0000.txt format and can be found here:


Additional new sequences are documented at
mrob.com/pub/math/nu-sequences.html where they are listed in the
lexicographical order as in Sloane and Plouffe's 1995 book. (An example is
0, 0, 0, 1, 1, 2, 4, 7, 16, 46, 174, 3311, 268446771,
401906756202069927727330981, ... an exponential recurrence relation.)

When creating the header for this new data file I realized the sheer volume
of original work I have created over the past 20 years, with many
illustrations and cross-references, to augment the OEIS. Many of you have
commented favorably on these pages and I suspect there is much more you
might like, on subjects that simply haven't come up in discussions recently.

So here is that portion of the header, listing my web pages by topic:

I have many web pages related to sequences; including:
( www.mrob.com/pub/math/ then )

  nu-sequences.html   A listing of all the sequences I have worked on
  seq-linrec2.html    2nd-order linear recurrence sequences
  MCS.html            A broad and complete listing of recurrence
sequences ranked by formula complexity

  seq-coprime.html    Mutually coprime sequences
  seq-cullen.html     Generalized Cullen and Woddall numbers
  seq-wondrous.html   Related to Collatz 3X+1 iteration
  seq-narayana.html   The Narayana triangle and several related triangles

  seq-kaprekar.html   Kaprekar sequences
  seq-mandelbrot.html A few special sequences related to the
Mandelbrot Set (more at

Here are pages on specific sequences that are particularly notable (lots of
original work, pretty illustrations, etc.)

  seq-a000215.html    Fermat numbers
  seq-a001181.html    Baxter permutations
  seq-a002061.html    Hogben's Centered Polygonal Numbers

  seq-a005646.html    Classifications of N Elements
  seq-a006542.html    C(n,3)C(n-1,3)/4
  seq-a019296.html    exp(pi*sqrt(N)) is nearly an integer
  seq-a019473.html    Still-Lifes with N cells in Conway's game of Life

  seq-a020916.html    "Molecules" -- a restricted class of permutations.
  seq-a023394.html    Prime Factors of Fermat Numbers
  seq-a045619.html    Product of 2 or more consecutive integers
  seq-a052154.html    Coefficients of Lemniscates for Mandelbrot Set,
or Binary Trees of Limited Height

  seq-a064224.html    Two Distinct Representations as Product of Integers>1
  seq-a082897.html    Perfect Totient Numbers
  seq-a092188.html    Smallest Positive Integer M such that
2^3^4^5^...^N == M mod N
  seq-a094358.html    2^^N == 1 mod N, or Squarefree products of
factors of Fermat numbers

  seq-a094534.html    Centered Hexamorphic, or Automorphic Hexagonal, Numbers
  seq-a100140.html    Largest Denominator of Greedy Egyptian Fraction for M/N
  seq-a160818.html    Equal to Average of Permutations of its Digits

  seq-a162002.html    2^^N == 2^(2^N) modulo N

The following also contain many illustrations and background material
related to sequences:

  numbers.html        Numbers (note in particular the entries for the
numbers: 14, 21, 27, 29, 61, 66, 158, 2.003..*10^19728)

  largenum.html       What happens when you try to beat the integers
in a race towards infinity

To illustrate the data format, here are two entries. In the first, the %S
field overrides that in OEIS and the other fields augment the record. The
other has a completely new A-number. In both the new %d field aids automatic
determination of which version is newer.

%d A005646 20091227.130727
%S A005646 1,1,1,3,6,26,122,1015,11847,208914
%C A005646 Extensive explanation with illustrations on Munafo web page.
%C A005646 This sequence is the row sums of triangle A171871.

%H A005646 R. Munafo, <a
href="http://mrob.com/pub/math/seq-a005646.html">Classifications of N
%Y A005646 Cf. A000055, A171872, A171873.

%E A005646 1015 term from Andrew Weimholt, Dec 15 2009
%E A005646 11847 term from Andrew Weimholt, Dec 19 2009
%E A005646 208914 term from Robert Munafo, Dec 29 2009

%d A171871 20091230.120130
%I A171871

%S A171871 1,0,1,0,0,1,0,0,1,2,0,0,0,3,3,0,0,0,3,17,6,0,0,0,1,36,74,11,0,0,
%T A171871 0,1,60,573,358,23,0,0,0,0,56,2802,7311,1631,47,0,0,0,0,50,10087,
%U A171871 107938,83170,7563,106,0,0,0,0,27,26512
%O A171871 0,10

%N A171871 Triangle read by rows: Distinct classifications of N
elements containing exactly R binary partitions
%C A171871 Row N has N terms in this sequence. The triangle starts:
%C A171871 1
%C A171871 0,1
%C A171871 0,0,1

%C A171871 0,0,1,2
%C A171871 0,0,0,3,3
%C A171871 0,0,0,0,3,17,6
%C A171871 0,0,0,0,1,36,74,11
%C A171871 Value is 0 for all (N,R) for which N is greater than 2^R.
%C A171871 Each term A(N,R) can be computed most efficiently by first
enumerating all classifications in A(N-1,R) plus those in A(N-1,R-1).

%H A171871 R. Munafo, <a
href="http://mrob.com/pub/math/seq-a005646.html">Classifications of N
%Y A171871 Cf. Row sums are A005646.

%Y A171871 Cf. Column sums are A171832.
%Y A171871 Last term in each row is A000055[N].
%Y A171871 Same triangle read by columns is A171872
%A A171871 Robert Munafo, Dec 29 2009

 Robert Munafo  --  mrob.com

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