Page maison de Simon Plouffe

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
                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 formula

algebraic number

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

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
formulas for primes

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)

Articles and other documents
Recent articles on the ArXiv site
or the Vixra site
images of distribution modulo 1
Experiments modulo 1
Generating Functions of the OEIS
films from the OEIS database
Integer relations

From the OEIS database
Distribution mod 1

Experience #2

N*k^n mod M

Integer Relations
Inspired formulas
basés sur les suites de l'OEIS

old articles
Lots of math books here
OEIS rational fractions
OEIS recurrences
Sequences to real numbers tables

Reverse of numbers : lots of graphics
k^n : what is the limit point ?
Bigger images herebinomials
Experiments in 1974-1981, original prints