BBP-type formulas — An elementary approach

Simon Kristensen*, Oskar Mathiasen

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


We provide a simple way of searching for formulas of the Bailey–Borwein–Plouffe type together with an algorithm and an implementation in sage. Aside from rediscovering some already known formulas, the method has been used in the discovery of a new BBP-type formula for 3π. In addition, the implementation is very flexible and allows us to look for BBP-type formulas to irrational bases. As an example of this, searching in various Pisot bases, we have discovered a formula for π in base 1+3, along with additional formulas.

Original languageEnglish
JournalJournal of Number Theory
Pages (from-to)251-263
Number of pages13
Publication statusPublished - Mar 2023


  • BBP-type formulas
  • Formulas for π
  • Null formulas


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