Page maison de Simon Plouffe Home Page

La tête pleine de chiffres / A head full of numbers
disponible sur amazon
page 1 francaispage 1 english

A formula for the n'th digit of π\pi
Pi with Euler numbers
and Pi in binary
Pi in
                binary with bernoulli numbers

The shape of b^n mod p
Shape of b^n mod p

Time line

1983 :arctan_of_1_2_over_pi
1991 : First version of GFUN

1992 : expPi-Pi

1992 : The n'th Tribonacci number is : tribonacci

  1992 :Master Thesis : Approximation de fonctions génératrices et quelques conjectures

1993 : A sequence related to that of Thue-Morse
1993 : Exact formulas for integer sequences

1995 : BBP
1995 : Publication de : The encyclopedia of Integer Sequences
1995 : Ouverture du Inverse Symbolic Calculator

1996 : Algorithm for Pi in base 10

1996 : Computation of the 10000'th Bernoulli number (with Greg Fee)
1998 : Ouverture de l'Inverseur de Plouffe - Plouffe Inverter

1998 : Integer relations :


2001 : Fibonacci numbers and plants (and other radio and tv)

2001 : Computation of the  750000'th Bernoulli number

2006 : New formulas for Pi and 1/Pi : pi 2006

2006 : Experiments modulo 1:


n2^n mod

2010 :Interesting approximations approximation of 119 and 10

2011 : A formula for the mass ratio of the neutron/proton :

neutron/proton mass ratio

2011 : 148000 empirical formulas found in the OEIS database

2014 : Strange formula for some algebraic numbers: algebraic

algebraic number

2014 : A formula for the Zeta function : formula for the zeta

wave in
              the zeta zeros

2015 : A formula for the proton/electron mass ratio:
mass ratio of proton and electron

2016 : Formula for primes using irrational numbers

2016 : Portable version of the Plouffe Inverter : Version portable de l'Inverseur de Plouffe. 11.3 billion entries at 41 digits precision.
2022 : A formula for the n'th digit of Pi (decimal or binary)
2023 : Pi and the primes
2023 : Efficient formulas for Zeta(2n+1)
2023 :
OEIS conjectured formulas
Other tables and graphics:
Binary  expansion of 4th degree algebraic numbers
Generalized expansion of real numbers
Integer Relations graphics
Les nombres de Fibonacci et les plantes
Prime numbers in different bases
Lots of graphics
Other graphics mod 1
Old graphics made by hand
OEIS formulas extended with rational fractions
OEIS with recurrences
OEIS graphs
Numbers reverses in graphics