Wednesday, November 24, 2010

Proof - a phenomenological touch

A phenomenological perspective on proof theory: of a particular interest here is a view on the proof as "fulfillment of a mathematical intention". See Richard Tieszen, Phenomenology, Logic, and the Philosophy of Mathematics, CUP, 2005, Ch. 13 - "Proofs and fulfillable mathematical intentions" (a  book which also addresses Kurt Gödel's involvement with phenomenological thought - also see Giuseppina Ronzitti's review in Philosophia Mathematica 16(2),264-276, 2008).

Monday, November 1, 2010

New paper. GPF-Tribonacci sequences

Starting with 5, 13, 7, each subsequent term is the greatest prime factor of the sum of the previous three terms. More about this type of sequences - in a new Fibonacci Quarterly article by Greg Back and Mihai Caragiu ("The Greatest Prime Factor and Recurrent Sequences" - Fibonacci Quarterly 48 (2010), no. 4, 358–362) - abstract here. 

In the main result on GPF-Fibonacci sequences (Theorem 3) we prove that all GPF-Fibonacci sequences (that is, prime sequences in which each subsequent term is the greatest prime factor of sum of the previous two terms) that are non-constant eventually enter the same 4-cycle 7,3,5,2.