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# User:Jaume Oliver Lafont/Topics

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## Contents

## Sequences submitted

### Logarithms

- A154920 Denominators of a ternary BBP-type formula for ln(3)
- A155988 (2n+1)9^n
- A164985 Denominators of ternary BBP-type series for log(5)
- A165132 Primes whose logarithms are known to possess ternary BBP formulas
- A166711 Permutation of the integers: two positives, one negative
- A166871 Permutation of the integers: 3 positives, 2 negatives
- A157024 a(0)=1, a(n)=(3n-1)3n(3n+1)/2 for n>0
- A165283 (2n+1)16^n
- A166486 Periodic sequence [0,1,1,1] of length 4
- A167407 T(m,n) is -m if n=0, 1 elsewhere
- A166725 (2n+1)25^n
- A165998 Denominators of Taylor series expansion of 1/(3*x)*log((1+x)/(1-x)^2)
- A157718 Greedy Egyptian fraction expansion of log(3)

### Pi

- A157142 Denominators of Leibniz series for Pi/4
- A156269 Denominators of a series expansion for Pi/2
- A156618 Denominators of Egyptian fraction for Pi-3 whose partial sums are the convergents
- A157332 Denominators of Egyptian fraction for Pi/16 based on Machin's formula
- A154633 (4n+1)(4n+3)(4n+5)(4n+7)
- A154956 Pierce expansion of 2/Pi
- A155482 Signed-digit binary expansion of Pi/4
- A155996 Nearest integer to 2^n*Pi/4
- A156736 Signed greedy Egyptian fraction for Pi/2
- A156750 Greedy Egyptian fraction for Pi/2
- A157327 Egyptian fraction expansion for Pi/4=atan(1/2)+atan(1/3) (Hutton 1776)
- A164916 Denominators of a BBP series for Pi/4
- A164924 Denominators of Egyptian fraction for Pi/4 whose partial sums are the convergents
- A155481 Signed-digit decimal expansion of Pi
- A156240 Nearest integer to 16^n/(Pi-3)
- A157193 Greedy Egyptian fraction expansion for 4/Pi
- A156790 Number of first quadrant lattice squares inside the circle x^2+y^2=(2^n)^2

### e and e^Pi

### Factorization

- A157017 Numbers n such that n! can be written as a product of distinct factors in the range from n+1 to 2n, inclusive
- A157612 Number of factorizations of n! into distinct factors
- A157625 Product of the composite numbers between n+1 and 2n, both inclusive.
- A157672 Number of unordered factorizations of n! into two distinct proper factors.
- A165259 Sum of odd powers of 4 and 9 divided by 13
- A165443 a(n) = ( 16^(2n+1) + 81^(2n+1) )/97
- A165448 Product of prime numbers between 2^n+1 and 2^(n+1), inclusive.
- A158366 Least k such that n! divides (n+k)!/(n+1)!
- A167205 (3^n+1)/(3-(-1)^n)

### Rational recurrences

- A165903 (a(n-1)^2+a(n-2)^2+a(n-1)*a(n-2))/a(n-3)
- A165896 a(n) = (a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)*a(n-2)+a(n-1)*a(n-3)+a(n-2)*a(n-3))/a(n-4) with four initial ones
- A165904 Somos-4 recurrence with a(i)=2^i for 0<=i<=3
- A165905 Somos-4 recurrence with a(0)=1, a(1)=2, a(2)=4, a(3)=16

### Time-variant recurrences

### Graph coloring

- A158411 Maximum number of colors required to paint a map having n regions
- A158478 Number of colors needed to paint n sectors of a circle
- A158515 Number of colors needed to paint a wheel graph on n nodes
- A158799 a(0)=1, a(1)=2, a(n)=3 for n>=2