Counting Sheep or Sums of Primes

 

(Image: Creative Commons — Attribution-ShareAlike 3.0 Unported — CC BY-SA 3.0 Washaweb on Iconfinder)

The other night, I had trouble getting to sleep. Instead of counting sheep, I challenged myself to adding the first n primes. The first 10 primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Therefore, for the n=1 through 10, the sums of the first n primes are: 2, 5, 10, 17, 28, 41, 58, 77, 100, 129. 

I was interested in any pattern exhibited by the sequence. After n=10, I became less confident in my ability to add late at night and then a comforting thought hit me. I realized one could easily research if others had explored this sequence by going to the website of The On-Line Encyclopedia of Integer Sequences® (OEIS®). This site was written about in a prior post: Math Vacation: What is the next number in the sequence...? (jamesmacmath.blogspot.com).

With the thought that my inquiry into the sequence could easily be answered, I fell asleep. Mission Accomplished.

The next morning, I simply entered 2, 5, 20, 17 into the site’s search bar and the following answer came up: A007504 - OEIS, The sum of the first n primes. With this sequence are links also related to sequences and references to those who have researched the sequence.

I invite readers to explore this rich resource at OEIS.