Mathematical Publications

 

Papers (mostly preprints)

*2007: Lineare Rekurrenzen, Potenzreihen und ihre erzeugenden Funktionen. Diese kurze Einführung in Theorie und Berechnung linearer Rekurrenzen versucht, eine Lücke in der Literatur zu füllen. Zu diesem Zweck sind viele ausführliche Beispiele angegeben. – This short introduction to theory and usage of linear recurrences tries to fill a gap in the literature by giving many extensive examples. [arXiv] *2004: Prove or Disprove. 100 Conjectures from the OEIS. Presented here are over one hundred conjectures ranging from easy to difficult, from many mathematical fields. I also briefly summarize methods and tools that have led to this collection. [arXiv] Some solutions can be found here. *Boring proof of a nonlinearity We prove classically, and step-by-step, that certain integer sequences satisfy the recurrence $a_{n-1}a_{n+1}=(a_n-1)^2$. [Postscript] *A recurrence for the fibonomials. An identity conjecture. [PNG at research.att.com] *2003: Proofs of some divide-and-conquer generating functions In this article, we give two independent proofs of the power series generating functions of the recurrence class $a_{2n}=\alpha a_n+c, a_{2n+1}=\alpha a_n+d$, one from the ground up, and one using a recently published lemma of the author. [Postscript] *Some divide-and-conquer sequences with (relatively) simple ordinary generating functions This is part II in the series 'Divide-and-conquer generating functions' and contains an overview of nearly all OEIS sequences of a certain type together with a collection of their ogfs. [HTML at research.att.com] *On the solutions to 'px+1 is square' In this short note, we construct the closed form of positive solutions to 'px+1 is square'. A short expression in terms of squares and triangular numbers is found. [Postscript] *Divide-and-conquer generating functions. I. Elementary sequences. Divide-and-conquer functions satisfy equations in $F(z),F(z^2),F(z^4)\ldots$. Their generated sequences are mainly used in computer science, and they were analyzed pragmatically, that is, now and then a sequence was picked out for scrutiny. By giving several classes of ordinary generating functions together with recurrences, we hope to help with the analysis of many such sequences, and try to classify a part of the divide-and-conquer sequence zoo. [arXiv] *On a sequence related to the Josephus problem. In this short note, we show that an integer sequence defined on the minimum of differences between divisor complements of its partial products is connected with the Josephus problem (q=3). [arXiv] *1999: Factors and Primes in two Smarandache sequences. About an application of number factoring. It appeared in the Smarandache Notions Journal 9(1998),4-10. [PDF] The subject of primes in similar numbers is one of the puzzles of primepuzzles. More recent information can be found on one of Eric Weisstein's pages at mathworld. http://arxiv.org/abs/0704.2481http://arxiv.org/abs/math.CO/0409509http://www.ark.in-berlin.de/conj-sol.pdfhttp://www.ark.in-berlin.de/A001110.pshttp://www.research.att.com/~njas/sequences/a010048conj.pnghttp://www.ark.in-berlin.de/dcgfproof.pshttp://www.research.att.com/~njas/sequences/somedcgf.htmlhttp://www.ark.in-berlin.de/A001082.pshttp://arxiv.org/abs/math.CO/0307027http://arxiv.org/abs/math.CO/0305348http://www.ark.in-berlin.de/sm.pdfhttp://www.primepuzzles.net/puzzles/puzz_008.htmhttp://www.primepuzzles.net/http://mathworld.wolfram.com/ConsecutiveNumberSequences.htmlshapeimage_1_link_0shapeimage_1_link_1shapeimage_1_link_2shapeimage_1_link_3shapeimage_1_link_4shapeimage_1_link_5shapeimage_1_link_6shapeimage_1_link_7shapeimage_1_link_8shapeimage_1_link_9shapeimage_1_link_10shapeimage_1_link_11shapeimage_1_link_12shapeimage_1_link_13