Try to solve these sequences

Hey everyone,

I brought you some clever and funny sequences try to find the next term to everyone

$\text{Sequence 1}$ : $1,11,21,1211,111221,?$

$\text{Sequence 2}$ : $10,11,12,13,20,?,1000$

$\text{Sequence 3}$ : $6,2,5,5,4,5,6,3,?$

$\text{Sequence 4}$ : $2,71,828,?$

Have fun

#Logic

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

For sequence 1, the sequence is $312211, 13112221, 1113213211, \dots$ . It is called "look-and-say" sequence, which has the property to describe the amount of same digits concatenating together, then concatenate that word with the digit itself.

For example, start with 1 (one 1s), 11 (two 1s), 21 (one 2s and one 1s), 1211 (one 1s, one 2s and two 1s), 111221 (three 1s, two 2s and one 1), 312211 (one 3s, one 1s, two 2s, two 1s) and so on. Notice that the next number is formed by concatenating the amount of that consecutive digit into the number itself

For sequence 2, see sequence A082492 at OEIS

For sequence 3, see sequence A006942 at OEIS

For sequence 4, it is $1828, 45904, 523536, \dots$ . It follows the significant figures of $e$ .

Kay Xspre - 5 years, 4 months ago

yes the first one is pretty famous. good job ^^

Abdeslem Smahi - 5 years, 4 months ago

Oh I know the third one

Thought of it sometime back

So, it basically represents the number of "line segments" that are used to display numbers on a calculator (As far as Ii know, all calculators have nearly the same display)

So, the next number is 7, which is the number of segments required to make the number 8.

Mehul Arora - 5 years, 4 months ago

Edit: I did not see @Kay Xspre 's solution which had the link to the series.

Mehul Arora - 5 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$