All kinds of mathematics
remind me of you
Lisbon, 24-27 July 2017

Peter Cameron's homepage

Welcome to my St Andrews homepage. Under construction This page is under construction (and probably always will be!)

I am a half-time Professor in the School of Mathematics and Statistics at the University of St Andrews, and an Emeritus Professor of Mathematics at Queen Mary, University of London.

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School of Mathematics and Statistics
University of St Andrews
North Haugh
St Andrews, Fife KY16 9SS
Tel.: +44 (0)1334 463769
Fax: +44 (0)1334 46 3748
Email: pjc20(at)st-arthurs(dot)ac(dot)uk
  [oops – wrong saint!]

Page revised 10 December 2016

A problem

A zero-one sequence is called universal if every finite zero-one sequence occurs as a (consecutive) subsequence of it.

Let s be the sequence whose nth term is 0 if the nth odd prime is congruent to 1 (mod 4), and to 1 if the nth odd prime is congruent to 3 (mod 4). Is s universal?

Unless I am missing something, this is probably a hard problem; but in view of the theorem of Green and Tao, it might be worth revisiting.

Old problems are kept here.