#online encyclopedia of integer sequences

[oeistournament]

Announcement: OEIS Tournament

OEIS Tournament Submission Form

This is @pc36thorn. Recently, I had the idea to do a poll bracket tournament on Tumblr with sequences from the OEIS (On-Line Encyclopedia of Integer Sequences). To determine the competitors, I will be accepting submissions. I have not yet decided how many competitors there will be, or when to cut off submissions. The rules for submissions are in the Google Form linked above. Seeding will be determined by how many submission a sequence gets, so don't be afraid to submit all your favorites even if they might have already been submitted.

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I was thinking about the Fibonacci sequence and how cool it is, but did you know that there are lots of other integer sequences as well?

With the On-Line Encyclopedia of Integer Sequences, you can search any finite sequence of integers and the OEIS will give you any known integer sequences containing that subsequence, complete with formulas, related references, and more!

[somethingusefulfromflorida]

On-line Encyclopedia of Integer Sequences

A006880 Number of primes < 10^n

0, 4, 25, 168, 1229, 9592, 78498, 664579, 5761455, 50847534, 455052511, 4118054813, 37607912018, 346065536839, 3204941750802, 29844570422669, 279238341033925, 2623557157654233, 24739954287740860, 234057667276344607, 2220819602560918840, 21127269486018731928, 201467286689315906290 

There are 0 primes below 10^0 (1)

There are 4 primes below 10^1 (10)

There are 25 primes below 10^2 (100)

etc.

This shows that primes become less frequent as you go on

40% of numbers under 10 are prime

25% of numbers under 100 are prime

16.8% under 1,000

12.29% under 10,000

9.592% under 100,000

7.8498% under 1,000,000

etc.

3, 5, and 7 are the only numbers below which a majority are prime, though 2, 4, 6, and 8 come close.

not prime (0/1, 0%)

prime (1/2, 50%)

prime (2/3, 66.6...%, highest percentage of primes)

not prime (2/4, 50%, most common percentage of primes)

prime (3/5, 60%)

not prime (3/6, 50%)

prime (4/7, 57.142857...%)

not prime (4/8, 50%)

not prime (4/9, 44.4...%)

not prime (4/10, 40%)

prime (5/11, 45.45...%)

not prime (5/12, 41.6...%)

prime (6/13, 46.153846...%)

not prime (6/14,  42.857142...%)

not prime (6/15,  40%)

not prime (6/15, 37.5%)

prime (7/17, 41.17647059...%)

not prime (7/18, 38.8...%)

prime (8/19, 42.10526316...%)

not prime (8/20, 40%)

not prime (8/21, 38.0952381...%)

not prime (8/22, 36.36...%)

prime (9/23, 39.13043478...%)

not prime (9/24, 37.5%)

not prime (9/25, 36%)

not prime (9/26, 34.61538462...%)

not prime (9/27, 33.3...%)

not prime (9/28, 32.142857...%)

prime (10/29, 34.4827586207%)

not prime (10/30, 33.3...%)

This post has no larger point, I just wanted to show this off