21

Number
$21$ (twenty-one) is:


 * $3 \times 7$


 * The $6$th triangular number, after $1, 3, 6, 10, 15$:
 * $21 = 1 + 2 + 3 + 4 + 5 + 6 = \dfrac {6 \times \left({6 + 1}\right)} 2$
 * Thus $21$ is the number of pips on a die.


 * The $3$rd octagonal number, after $1, 8$:
 * $21 = 1 + 7 + 13 = 3 \left({3 \times 3 - 2}\right)$


 * The $7$th semiprime after $4, 6, 9, 10, 14, 15$:
 * $21 = 3 \times 7$


 * The $8$th Fibonacci number, after $1, 1, 2, 3, 5, 8, 13$:
 * $21 = 8 + 13$


 * The $7$th lucky number:
 * $1, 3, 7, 9, 13, 15, 21, \ldots$


 * The smallest number which can be expressed as the sum of at most $3$ triangular numbers in $4$ ways:
 * $21 = 15 + 6 = 15 + 3 + 3 = 10 + 10 + 1$


 * The $4$th after $0, 1, 3$ of the $5$ Fibonacci numbers which are also triangular.


 * The $1$st of the $5$ $2$-digit positive integers which can occur as a $5$-fold repetition at the end of a square number, for example:
 * $508 \, 853 \, 989^2 = 258 \, 932 \, 382 \, 121 \, 212 \, 121$


 * The number of parts in the smallest perfect square dissection of an integer square.


 * The $4$th positive integer $n$ after $4, 7, 15$ such that $n - 2^k$ is prime for all $k$


 * The $14$th positive integer after $2, 3, 4, 7, 8, 9, 10, 11, 14, 15, 16, 19, 20$ which cannot be expressed as the sum of distinct pentagonal numbers.

Also see

 * Smallest Number Expressible as Sum of at most Three Triangular Numbers in 4 ways
 * Smallest Perfect Square Dissection
 * Square of Reversal of Small-Digit Number