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  User:Peter Luschny
  From OeisWiki
  Personal
  - Some of my mathematical interests can be found on my homepage.
  - My favourite sequence is A057641.
  - My favourite integer is 32760. Why? See here.
  - My favourite sentence is: "Integers are the decategorification of finite sets."
  - My favourite fun formula (which I found in 2010) relates Euler's small gamma A001620 with Euler's big Gamma and computes another constant which is also in OEIS.
  - (NEW in 2011, now discontinued.) You can follow me on sequitter.
  - In my contributions I follow Schmidhuber's Beauty Postulate: "Among several patterns classified as "comparable" by some subjective observer, the subjectively most beautiful is the one with the simplest (shortest) description, given the observer's particular method for encoding and memorizing it." "For example, mathematicians find beauty in a simple proof with a short description in the formal language they are using."
  - If you have any comments or suggestions, you can post them on my user talk page.
  Topics on OEIS
  My BLOG on OEIS
  Blog means that I try to explain the background of some sequences which I submitted to OEIS.
  I republished the article on Eulerian polynomials as a MathML document. You can find this version and some hints for creating web-pages with mathematical content on this page.
  Sequential musings
  Most coherent themes for which I have contributed sequences
  Some other themes I took interest in
  Stirling's famous formula and company
  More about these formulas can be found on my homepage and on my blog.
  On the infrastructure of the binomial triangle
  This is a symbolic representation of an infrastructure of the binomial triangle characterizing primes. A formal description of the idea can be found in A182929.
  An index of generalized Stirling triangles
  Two convenient indices of generalized Stirling triangles. I intend to add cross references on the sequence pages.
  Tagging Matryoshka sequences
  Elementary cases
  seq means sequence. alpha is typically 0 or 1. beta is a convenient number greater alpha. op is an operation to be specified.
  Matryoshkas of functions
  The elementary cases above are Matryoshka sequences related to the identity function. In the general case the innermost sequence seq(i,i=a..b) becomes seq(f(i),i=a..b). This relates sequences in a new and sometimes surprising way.
  With Maple:
  T0 := proc(op,f,a,b) local i; seq(f(i),i=a..b) end; T1 := proc(op,f,a,b) local k; seq(op(f(i),i=a..k),k=a..b) end; T2 := proc(op,f,a,b) local n; seq(op(op(f(i),i=a..k),k=a..n),n=a..b) end; T3 := proc(op,f,a,b) local m; seq(op(op(op(f(i),i=a..k),k=a..n),n=a..m),m=a..b) end;
  Example calls:
  T3(mul,n->n,1,7); T2(seq,n->n,0,4); T1(add,n->n!,0,7); T1(mul,n->n!,1,7); a := n -> `if`(n=0,1,n^(n mod 2)*(4/n)^(n+1 mod 2)*a(n-1)); T2(mul,a,1,7);
  Here some findings:
  Using MathJax on the OEIS-wiki
  To use MathJax on the OEIS-wiki proceed as follows: (1) Install the StiX fonts on your system. (2) Install the browser add-on Greasemonkey. For example for Firefox it is here: (3) Put the user script below in a file named mathjax.user.js. Install the script. More information here: (4) Test (5) Adapt if necessary: Place the mouse on a formula, open the context menu with a right click and set (for instance) Settings/ScaleAllMath to 112.
  // ==UserScript== // @name MathJax on OEIS // @namespace // @description Insert MathJax into OEIS-wiki.src = ""; var config = 'MathJax.Hub.Startup.onload()'; if (window.opera) {script.innerHTML = config} else {script.text = config} document.getElementsByTagName("head")[0].appendChild(script); } }