Is there a name for this number sequence?

Factual Questions
1

Where every entry is repeated the number of times it states?

1 22 333 4444 55555 666666 7777777 88888888…

2

Not that I know of. A bit of googling turned up Smarandache Sequences, which I admit I’d never heard of.

It did remind me a little of the Look-and-say sequence.

3

Here’s its “official” entry in the “official list” of all known mathematically “interesting” integer sequences: A002024 - OEIS.

For more about the sequence catalog itself see On-Line Encyclopedia of Integer Sequences - Wikipedia.

In common with the vast majority of mathematically “interesting” sequences, it doesn’t have a recognized name.

4

I’m not clear on what the sequence in question is. In the OP it looks like you have 8 numbers, where the n-th number contains n digits. But LSL interpreted it as 36 single-digit numbers. If my interpretation is correct, the OEIS sequence is A000461.

5

A Google search suggests this is called “n concatenated n times” sequence or sometimes called a Smarandache sequence.

6
  • 1 (one “1”)
  • 22 (two "2"s)
  • 333 (three "3"s)
  • 4444 (four "4"s)
  • 55555 (five "5"s)
  • …and so on
7

I think the question was whether the OP meant 1, 2, 2, 3, 3, 3, … or 1, 22, 333, …. I wasn’t sure either. but either way I didn’t know of a name for it.

8

You’re right. I was wrong. Total brain-fart on my part first thing in the morning before the coffee had sunk in. I glanced at the OP then dove right into the OEIS wanting to be first. Dumbshit move.

Sorry to mislead anyone / everyone.

9

It’s nice to see every freaking number sequence in the universe has a number. I wonder how often someone thinks up a new sequence?

Paper money collectors search for numerous sequences in the bill’s serial number but they all have nicknames. Bookend, repeat, radar, binary, staircase, birthday, etc. I have three birthday bills. The last digits of the serial number form a birthday or anniversary date that people might want to own, such as 691975 - June 9th, 1975. If you find the US birthday, 7-4-1776 that would be quite valuable.

10

The OEIS Welcome page says

During this period, from 1996 to 2009, the database grew by at least 10000 entries per year (18000 new sequences were added in 2009 alone).

but I don’t see any more details about its growth or anything more recent.