# This number sequence has entered my life recently

Just recently, I've noticed this sequence of numbers has become a pretty big part of my life. It goes like this:

1, 2, 4, 6, 9, 12

So here's the mystery:

• What is this sequence?
• Where do I keep seeing it?
• What comes next?
• Is there a formula for finding the next one?

Here's some clues if you're stuck:

When I say I've seen it recently, since the 23rd of March. (I live in the UK)

The only time I see this go past 4 is on Sunday Mornings.

• Boris Johnson addressed UK on 23rd March 2020. Does that give me some lead in the question?? – Lakshay Sura Jul 6 '20 at 14:31
• Also are you sure that it is only related to mathematics?? Or some another tag would be appropriate for this?? – Lakshay Sura Jul 6 '20 at 14:41
• @LakshaySura There may well be a link to the 23rd of March. I can't think of another tag which would be more appropriate. – AJFaraday Jul 6 '20 at 16:02
• @AJFaraday this is something related to rot13(inppvangvba sbe onol) ? – Swati Jul 7 '20 at 4:00
• Are you sure that it always goes past 4 on Sunday Mornings or are you saying on the basis of some sort of trend for eg.rot 13(Pnfrf bs Pbebanivehf va Hx)?? – Lakshay Sura Jul 7 '20 at 12:35

@athin has found the mathematical pattern in the sequence and created a useful general way to display it pictorially (go see their post and upvote). However, a slightly more accurate diagrammatic rendering would be as follows:

This is because the sequence reflects:

The size of sequential regular rectangular arrangements of participant windows in a video conference call.

The significance of 23 March in the hints is that:

This was the day of the stay-at-home government order from UK Prime Minister Boris Johnson that led to the first closures of workplaces due to the threat of coronavirus in the early days of the pandemic. From this date many workers in the UK - the OP included, presumably - began working from home and using video-conferencing software (like Zoom, Skype, MS Teams, etc.) with much greater frequency, in order to attend meetings with office mates and colleagues in disparate locations.

The pattern emerges as:

the number of participant windows visible on-screen increases. Usually these appear in a space-efficient visual grid, making optimal use of the space available on-screen (while preserving the relative dimensions of each individual window as closely as possible). The given sequence of 1, 2, 4, 6, 9, 12 represents grids of 1×1, 1×2, 2×2, 2×3, 3×3 and 3×4. The next term in the sequence would be 16 as the grid resizes to 4×4...

Note that in many of the main video-conferencing software packages (like Zoom) the sequence would terminate at 25, since at this point the extra attendees would begin appearing on a second 'overspill' page, so as not to result in the participant windows becoming too small to be usefully seen on the screen.

Why does the sequence only pass 4 on a Sunday morning? Possibly because:

The OP works in a small company with few close colleagues, never attending particularly large meetings during the week. However, on a Sunday they attend a virtual religious service online using similar video-conferencing software but with many more participants from a local church, mosque or temple congregation!

Here's hoping this sequence can be seen no longer very soon. Stay well and keep safe! :)

• This is completely correct and very thoroughly described, nice work! – AJFaraday Jul 7 '20 at 20:47
• Oh! I thought Sunday Morning is a news program lol. Anyway, very clever and nice! – athin Jul 8 '20 at 1:08

The sequence can be visually illustrated as the following:

For the mystery part, it also somewhat illustrates:

The pandemic i.e. the spread of the virus. It starts with one point, then it spreads horizontally and vertically (going right, down, left, then up).

The formula of the sequence is:

$$\lceil\frac{n}{2}\rceil \times \lceil\frac{n+1}{2}\rceil$$, which basically alternates between a square or a rectangle which its lengths differ by one.

• How does it relate to the second clue?? – Lakshay Sura Jul 7 '20 at 2:08
• @LakshaySura Maybe OP keep seeing it on the news, as answered in the second spoiler block. Or, tbh actually this sequence is very well-known thus actually it does appear everywhere. – athin Jul 7 '20 at 2:13
• But why on earth does OP see it going past 4 on Sunday?? Well a bit creative answer as it addressed the 23rd March thing as Boris Johnson addressed UK on that day about Coronavirus. – Lakshay Sura Jul 7 '20 at 2:14
• @LakshaySura Ah sorry, you mean that second clue in the spoiler. Actually I don't know about that, plus it is kinda UK-centric so perhaps, as a non-UK (and non-US) person, I won't have any idea.. :( – athin Jul 7 '20 at 2:17
• The sequence is right! You have the right set of current events, the date is when the UK went in to lockdown. However the pattern is not visualising the spread of the virus. You’ve got the maths right, too, just not what it is. – AJFaraday Jul 7 '20 at 7:07

Congratulations, I am assuming you have recently become a mother/father. These are the ages, in months, that doting parents use when someone asks "how old is he/she". If I remember correctly, the next one is 18, after which the series steps back to 2,3,4...(in years).

• How can you explain the second clue? A baby can only be older than four months on Sunday mornings? That would make for an interesting society lol – user46002 Jul 7 '20 at 4:03
• Because the child (born on 23 March) is still less than 3 1/2 months old, so only 1,2, and 3 will be used when the poster is talking about their own child (or 4 if talking to their neighbors who have a slightly older child). But on Sundays they go to the park where they find other families with older babies. All very logical you see... – Penguino Jul 7 '20 at 4:33
• I really like your thinking, Penguino, and I am indeed a father, but a father of only one and she’s 20 months old. I’m afraid this is not the answer. – AJFaraday Jul 7 '20 at 7:02

This pattern works as follows: first you start with 1 and in your sequence you add 1 once, then you add 2 twice in a row and then 3 three times in a row and so on ... Here: 1 + 1 = 2 (one time) 2 + 2 = 4 4 + 2 = 6 (two times) 6 + 3 = 9 9 + 3 = 12 (the sequence is incomplete, but the next is :) 12 + 3 = 15 (three times) 15 + 4 = 19 19 + 4 = 23 23 + 4 = 27 27 + 4 = 31 (four times) This is the first question and the third.The second is because you are a smart person who can see patterns even when they doesn't look like a real thing. The fourth question is probably yes, but i don't know how haha.

• Good attempt but I think this isn't the intended answer by OP. Do try to find significance with real life situation. – Lakshay Sura Jul 6 '20 at 17:38
• Also what significance do it have with 23 March – Lakshay Sura Jul 6 '20 at 17:39