5050
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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 $1$, $(10)$, $45$, $136$, $325$, $666$, $1225$, $2080$, $3321$:
- $5050 = \ds \sum_{k \mathop = 1}^{10^2} k = \dfrac {10^2 \paren {10^2 + 1} } 2$
- 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 $1$, $3$, $6$, $10$, $15$, $\ldots$, $4095$, $4186$, $4278$, $4371$, $4465$, $4560$, $4656$, $4753$, $4851$, $4950$:
- $5050 = \ds \sum_{k \mathop = 1}^{100} k = \dfrac {100 \times \paren {100 + 1} } 2$