Main is @eri-pl. This blog is for things that are not Tolkien-adjacent enough, (except some things that are profound or related to my mutuals so they go on main anyway + occasional (=very common) reblogging mistakes, because I can't use multiple blogs properly).
Your post about Wythoff array reminded me of a problem you might like. (Spoiler: I have an experimentally guessed formula, but no proof. Also, the formula is weird and kinda ugly.)
For each pair of positive integers (k,l) let's consider all the Fibonacci-like sequences (by "Fibonacci-like" I mean: a[n+1]=a[n]+a[n-1]) starting with a[0] being at most k, and a[1] being at most l (we are generally in the positive integer world. except the indices. Indexing things from zero is the only proper way.).
So, for example if k=2, l=3, we have these 6 sequences:
1, 1, 2, 3, 5,..
2, 1, 3, 4, 7, ...
1, 2, 3, 5, 8,...
2, 2, 4, 6, 10, ...
1, 3, 4, 7, 11,...
2, 3, 5, 8, 13, ...
Now let's look at the smallest positive integer not occurring in these sequences for a given k and l. Here in the example it is 9.
Define f(n) = the smallest such integer for the sequences when k=n and l=n. So to rephrase it: f(n) is the smallest positive integer non occurring in any Fibonacci-like sequence starting with two positive integers no greater than n.
It starts with 1, 4, 9, 17, 25, 38... (Also, it does have an OEIS entry, but quite inconclusive)
The goal is to find a formula for f(n). I mean, a nicer formula than the wall of text above.
I'm sorry for my informal wording, it's been long since I had a more formal contact with mathematics.
PS: the whole table for smallest numbers for all k and l, not only k=l looks very interesting too, and when you divide this number by k or l, you get pretty patterns:
(I love overusing spreadsheets for maths)
Hmmm…. This is interesting…
I haven’t came up with a proof yet, but I have some ideas on where to start!
First of all, any Fibonacci-like sequence starting with an and b is equivalent to aF_{n - 1} + bF_n, which can be shown by induction! Now, the problem can be simplified to solving diophantine equations with Fibonacci numbers.
This now reminded me of the Coin problem, since both relate to finding the minimum missing value. The problem is that in the coin problem, there are no bounds on an and b, so that makes this problem a bit harder. Maybe later on, I will look at proofs for the coin problem and see if I can generalize them to bounded an and b.
Thank you so much for the ask! The OEIS says that this problem has no proof, so I’m a bit unsure if I’ll be able to solve it, but I’ll give it my best go!
TBH I didn't expect you personally to fully solve it (especially not so quickly), but I hoped you'll like playing with it + I was curious about your thoughts on this + you are the math blog with the most audience (of all the math blogs i know) and I wanted to show this fun problem to math ppl of tumblr. :)
"Average man eateth 3 spiders a year" factoid veerily just statistical error. average man eateth 0 spiders per year. spiders georg, who liveth in cave & eateth over 10,000 each day, is an outlier adn should not have been counted
I had a dream last night that someone made sexy tumblr man humanizations of stuff like misogyny, homophobia, racism, etc and they all got really popular and people started making fanart and fanfics of them and shipping them and shit and someone made yaoi fanart of homophobia and misogyny and another user made a call out post for them.
was looking back through my blog to try and find an ask i answered and found this again and honestly the fact that this hasn’t come true is proof alone that we’re not in the worst timeline
it fucking sucks being a disabled person who can't work and having to see these fuckass posts where someone's like "ahaha jobless people have no life and that's why everyone shitty online has No Job" and everyone and their mother reblogs it joyfully onto my dash for me to see. yes unemployed and unemployable people are truly without exception dogshit people with no hobbies and no redeeming qualities. you're so right. anyway if you'll excuse me i have to start my shift at the I'll Never Be Employed Because Of Permanent Disability And I Love Knowing How You Really See Me store
btw this isn't solely a disability rights issue or an issue about people who are entirely unable to work. you should also be thinking about the people who are regarded as unhireable. transfems are hugely discriminated against in this way, people of color are passed over for less qualified white people, anyone who has any difficulty playing the interview game is less hireable... frankly anyone who made the mistake of pursuing the things they love and now has a degree for a niche field. if you still joke about Jobless People it's because you've fundamentally connected the worth of people to their labor, and specific labor, work that you see as valuable. and while i'm at it stop making fun of people who still live with their parents. asshole.
Honestly, Tvyek is pretty miraculous. It’s permeable to water vapor but not to water, it’s nearly impossible to tear, but can be easily cut. It’s cheap and made entirely without binding chemicals. In addition to being used for wristbands, it’s used to wrap construction sites to keep out water during construction, for tear-resistant envelopes at Fed-Ex, coveralls for mechanics, and my wallet, actually.
Fun tip, though it looks like paper, Tyvek is plastic, and cannot be recycled with paper.
A daily game that challenges our understanding of human cultures. Ten objects. 5,000 years of human history. Guess where and when each artif
An interesting game where you are presented with 10 artifacts from the MET. You have to place where the artifact is from and what time period it is from. Each artifact scores up to 10,000 points, and you lose points the further away your guess is and how far off in time you are. You can only play once a day. Thanks to @baebeylik for showing this to me.
Today I scored really well. Yesterday ... not so much.
Anthropeum.com · Jun 8 2026
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79,001 · top 3% of players today!
Here's some of the notes, starting with the things multiple people brought up:
SHRIMP COCKTAIL:
banahbanah: #flashback to that one fic where Peter Parker frets about drinking shrimp cocktail because of the alcohol
generaldeliciousness: adding: what a prawn/shrimp cocktail is
#why is your character turning it down because they're under 21 #do you think prawn cocktail is a cocktail #this lives in my brain rent-free constantly #the rest of the fic was so normal #and good enough that i'll still re-read it #but bro
And then many, MANY, people wondering if this was actually authour mistake, since Peter really would do this!
POMEGRANATES:
zhajhassa: #haha where's that post that was like someone describing someone eating a pomegranate but they ate it like an apple
thornhands: #once someone wrote persephone biting into a whole Pomegranate #had to stop and stare at a wall for a minute
sungsingsanguine: I once saw someone very confidently write about a character eating slices of pomegranate.
FRUIT TREES:
zagreuses-toast: #given a very endearing glimpse into a writers blindspots by seeing them describe someone sitting under a ''pineapple tree''
salatrash: I remember something about picking watermelons... OF A FUCKING TREE
baander: #cranberry trees
DOUGH/BATTER:
maycelium: #I'm a chef so I'm really used to people not accurately describing how to cook food #But I was surprisingly flabbergasted when someone was writing making a cake and was kneading it. Which uh #Not necessary for cake. It was interesting for sure but just bizarre
livebloggingmydescentintomadness: #the one that drove me nuts was when a character set aside a batch of PASTA DOUGH 'to rise' #pasta doesn't have yeast!! #it does need to REST but it will never RISE #you do not want an airy crumb on your noodles
lovesodeepandwideandwell: #THE ONE WHERE THEY MADE COOKIES BY LADLING BATTER INTO A TRAY
Some other topics:
ANIMALS:
catenarwhal: #mandatory 'how cows produce milk' mention#i'll never recover from that one I fear
piromantic: #one time i saw someone fake their way through describing how spiders behave
pluto-lichen: horses
misskittypotter: #stardew valley faking its way through what fresh fish smell like
pa-pa-plasma: #saw someone faking their way through knowing what a seal is once #i still am fucked up over that one to this day. they just straight up did not know #& they were NOT good at guessing it either like it was clear they had never googled that animal ever #& was only just now realizing via answering questions from anons that seals are not!! what they assumed. initially
SEX:
dykevandyke: #what a prostate is #and where it is located #as in. external.
dreamyeyedrose: #I remember back in the ff.net days reading an Ichigo/Renji fic where the writer assumed the penises go inside each other #and I was like “I mean I don't know how it works for sure I don't have one but idk if that's how it works”
SOME OTHER FOOD STUFF:
thetrekkiehasthephonebox: #add another one to the list bloggers#this character is cooking a salad
shosta: #still baffled about the published work that didn't know food could freeze
sun-dari: #once i read a fic where the author didn't understand cinnamon
alto-tenure: #read something recently where the author was just. blatantly wrong about spices
dramatic-dolphin: #i saw someone try to fake their way through what ramen is once. like 14 years ago.#but i remember.#i was very confused about ramen for a few months. they were writing it so authoritatively.
the-celery-stalks-at-midnight: #i will never ever forget someone putting leftover fries in the microwave to reheat them and setting the timer for five minutes
typeghost: #this sparked a memory of a hannibal fic where the author had to fake their way through writing about gravy
draculin: #the one fanfic where the author knows about coffee only as a concept wrote a character as a coffee drinker#was very interesting#I don't remember the fandom or the plot but I was mesmerized by the coffee actions and choices
11235811235811: #there's a lot of faking their way thru congee in the svsss fandom i'll also note
fishali3n: #read one where the person clearly didnt know what tofu is
emmy-everafter: #in the aftermath of shadow and bone s2 i saw a lot of people pretending to know what stroopwafels are #babes they are more like cookies than breakfast waffles #like yes there is a waffle pattern but you're not gonna cut into a stack of them with syrup and sugar#🤣🤣🤣
NON-FOOD STUFF:
red-umbrella-811: Shoutout to Dame Agatha Christie for faking her way through what a wrench is in a very popular published work.
bluebeetle: #once saw someone have a character put an entire phone book in their pocket
nonametis: #- sex talk in languages other than english #<- or just the petnames in a different language other than English
sadisticpony: #the fanfiction i saw this week where op DIDNT KNOW HOW AUTOMATIC DOORS WORKED #and that they arent in peoples homes!!! of course. also opening the automatic door for someone is unironically very funny but its not #its not like. grabbing the door handle to let someone in. helpppp
danmeichael: #reminds me of the fic with the figure drawing class where the character started with the feet. #i love you feet first figure drawing author
meowmix1100blr: #me watching this one fic absolutely obliterate what the board of directors does
vexedhexes: #one time i read an architect character making a doorway bigger by building a bigger door #what a beautiful world. #OH. also gravity falls fic where they go 'oh piedmont is in california so its warm all year round'
leveragehunters: #characters going to a beer garden #And it's literally a garden outside the pub#It was a very cute mistake
fitofpique: #yes! #grown men do not get blind drunk off two beers #but i am possibly guilty of the hypothermia one #assuming it does not make you very horny?
dadvans-likes: #always thinking abt the soup kitchen fic #the entire setting of the fic was 'soup kitchen' #and i very quickly realized #the author did not know what a soup kitchen was #and they thought that soup kitchens only served soup #fic
msmargaretmurry: #i love fanfiction #once read a fic where the characters played 20 questions #but the author seemed to not know how to play 20 questions and was just kind of winging it........ #immaculate
shakespeareaddict: #Look I know not all of us are hockey experts #But it takes about ten seconds of research or any attention paid to the show to realize #That the Stanley cup playoffs are not in fucking September
baejax-the-great: #the funniest one i saw #was someone faking what church is like #like 1. they really didn't have to write an entire church experience for their fic #and 2. they had clearly never even watched a show where people went to church #it was bonkers weird
twosunson: #things ive seen authors faking #knowing how to unclog a drain #knowing. literally any history #knowing what ketamine looks like (apparently- oregano) #(you know who you are)
waterhorseyblues-ao3: #beltane being celebrated in winter #wales being portrayed as a completely separated land from england (i wish) #characters getting up after weeks of bedrest like that dosnt completely fuck you up
violetfairydust: #i once read a fic where the flight time from london to seattle was 3 hours
purekesseltrash: One time, in a fic set specifically in Des Moines, IA, two of the characters casually drove 20 minutes to the ocean. The memory continues to delight me. I want to know where that author thought that Iowa was.
TBH maybe I understand the word "cake" wrong (I'm Polish) but there is a blurry line between some cakes and bread. And there are cakes which I do knead (especially my MIL's drowned Easter cake --- it has yeast of course)
Also, some salads involve cooking (chicken salad. You cook the chicken. At least in the variant we do.)
Also not a fic but a ttRPG, but: I saw someone assuming that a crochet hook is a kind of needle and you can effectively stab someone with it.
And I am totally faking A LOT in my writing (and I would fake more if I did not have a smart husband who can explain to me how thermobaric bombs work, or ships, or any of the boring military/sailing stuff... i'm an abstract person)
Also, society (because it's not the focus of the plot --- it's a near-utopia and the police is helpful and the state works and there is almost no sexism and a well-integrated multiethnic society. deal with it and focus on the morgoth and evil forests) and Tolkien languages (i do have some surface knowledge but I'm faking a lot) and whatnot
(I have, however, done some reading on how hypothermia works --- thank you pintrest. it will become relevant later)
I think part of getting better is complete ego death. Like you’re not above setting a timer for 5 minutes and focusing on a task. You’re not above doing a very simple 3 minute workout to start. You’re not above reading for 10 minutes a day when you first get out of your reading slump, even if you used to read for hours. You’re not above starting slow and then building up to where you want to be/where you once were. What you are above is total inertia. Doing something really is better than doing nothing. Radically accept where you are, radically accept your limits, and go from there. Don’t let your ego get in the way.
