OEIS Sequence of the Week [July 29, 2013]

A005235: Fortunate numbers: least  such that  is a prime number, where  is the product of the first  prime numbers:

3, 5, 7, 13, 23, 17, 19, 23, 37, 61, 67, 61, 71, 47, 107, 59, 61, 109, 89, 103, 79, 151, 197, 101, 103, 233, 223, 127, 223, 191, 163, 229, 643, 239, 157, 167, 439, 239, 199, 191, 199, 383, 233, 751, 313, 773, 607, 313, 383, 293, 443, 331, 283, 277, 271, 401, 307, 331

Problem of the Week [July 29, 2013]

For each positive integer , let  be the number of triangles with integer side lengths, positive area, and perimeter . For example,  since the only such triangle with perimeter 6 has side lengths 2, 2, and 2. Determine the smallest positive integer  such that .

Correct answers as well as solutions will be acknowledged.

Interesting Fact of the Week [July 29, 2013]

On December 16 1811, the Mississippi River began to flow backwards due to a powerful earthquake.

Equation of the Week [July 29, 2013]

The Fundamental Theorem of Calculus allows one to compute the definite integral of a function using any one of the infinitely many antiderivatives:

,

where  and  are real-valued functions on the interval , such that for all  in , 

.

Visual Art Piece of the Week [July 29, 2013]

Pablo Picasso's Three Musicians:

Classical Music Selection of the Week [July 29, 2013]

Franz Schubert's Piano Trio in E flat Major op. 100 D 929 2nd movement - Andante con moto:
http://www.youtube.com/watch?v=tKZBmMu06Fg

Quote of the Week [July 29, 2013]

Milord, I should be sorry if I only entertained them. I wished to make them better.

-George Frideric Handel