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#oeis 2026-05-22Here are some more whimsical OEIS sequences I came across.XKCD 2016 joked that “OEIS keeps rejecting my submissions,”
including one that gives “Integers in increasing order of width when printed in Helvetica.”
Well, two days after that comic was published (2018-07-09),
Hugo Pfoertner published A316600,
with a very precise definition.
Then he did Arial.Randall Munroe missed a huge opportunity to commit to his bit
and actually try to submit some of his sequences before publishing the comic.
Also, the graph for the sequence is rather fun.A366192 has a fun little secret.
It’s formally the complement of Cantor’s sequence A352911,
which enumerates reduced fractions to demonstrate their countability.
In other words, A366192 are all of the “non-reduced” fractions.Peter Luschny, who originally submitted this sequence,
titled it “Peter’s List: Fractions nobody needs (because they can be reduced to a simpler form).”
In the history he gave the justification:
“Georg has such a nice sequence (A352911), I wanted one like that too…”
I like that Peter is on a first-name basis with Cantor.There’s the “screaming sequence” A325911,
which are numbers whose hex representation is all “AAAAAA…”
There are the James Bond primes, A386240,
which all have “007” in their decimal representation.There are lots of random number tables, like
A259233, the
random table of bytes used by Doom; or
A357907, the internal state
of the ZX81’s RNG.There is a “nonsense sequence”, which,
I’m still not quite sure what it’s about.Then there are a lot of sequences about devils and “The Beast”?
Like A115983 which are primes that have 666 digits.
Or A186086 and A131645,
which have 666 as a particular substring.
Somehow I shudder to think what current-day children would do
with the prime 76667.Also, apparently the devil has a fax number? It’s 667.
A138563 are the “Beastly fax numbers.”
Neil Sloane described it in an interview,
as a sequence whose including in OEIS would be “going too far” towards whimsy.A few moments later in the interview, he remembered,
“Actually, the fax numbers of the beast are in.
I sent in the sequence myself.”OEIS entries have a keyword table.
When looking at these sequences, I noticed most share a keyword of “dumb.”
Indeed, you can search OEIS for dumb sequences
and maybe they should rename that keyword to “whimsical.”Want to respond? Send me an email,
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The author presents a collection of whimsical sequences found on the On-Line Encyclopedia of Integer Sequences (OEIS), drawing attention to the unusual and imaginative nature of these mathematical patterns. The text references sequences that have garnered attention for their peculiar properties, such as A316600, which was formally defined by Hugo Pfoertner. Another notable example is A366192, which is the formal complement of Cantor's sequence A352911, which enumerates reduced fractions, meaning A366192 lists the non-reduced fractions. Peter Luschny, who submitted this sequence, titled it "Peter’s List: Fractions nobody needs," justifying its existence by referencing Cantor’s sequence. The author notes a shared thematic element among many sequences, observing that most carry the keyword "dumb," suggesting that this term might be better renamed "whimsical" when applied to such entries, and notes that Neil Sloane described this tendency in an interview.

The text highlights several specific whimsical sequences. The author mentions the existence of the "screaming sequence," A325911, comprised of numbers whose hexadecimal representations consist entirely of the character 'A'. Other examples include the James Bond primes, A386240, which feature the digits '007' in their decimal representations. Random number tables, such as A259233, used for the random bytes in Doom, and A357907, representing the internal state of the ZX81’s random number generator, are also cited. Furthermore, the author discusses sequences related to themes of devils and the "Beast," including A115983, which are primes containing 666 digits, and A186086 and A131645, which feature 666 as a substring. A138563 is identified as the "Beastly fax numbers," which the author amusingly links to the number 667. The article concludes by noting that the inclusion of these sequences reflects a desire to explore more whimsical mathematical concepts within the established framework of OEIS.