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.
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