5050

Number
$5050$ (five thousand and fifty) is:


 * $2 \times 5^2 \times 101$


 * The total of all the entries in a magic square of order $10$, after $1$, $(10)$, $45$, $136$, $325$, $666$, $1225$, $2080$, $3321$:
 * $5050 = \displaystyle \sum_{k \mathop = 1}^{10^2} k = \dfrac {10^2 \paren {10^2 + 1} } 2$


 * The $13$th Kaprekar number after $1$, $9$, $45$, $55$, $99$, $297$, $703$, $999$, $2223$, $2728$, $4879$, $4950$:
 * $5050^2 = 25 \, 502 \, 500 \to 2550 + 2500 = 5050$


 * The $100$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $4095$, $4186$, $4278$, $4371$, $4465$, $4560$, $4656$, $4753$, $4851$, $4950$:
 * $5050 = \displaystyle \sum_{k \mathop = 1}^{100} k = \dfrac {100 \times \paren {100 + 1} } 2$