4950

Number
$4950$ (four thousand, nine hundred and fifty) is:


 * $2 \times 3^2 \times 5^2 \times 11$


 * The $99$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $4095$, $4186$, $4278$, $4371$, $4465$, $4560$, $4656$, $4753$, $4851$:
 * $4950 = \displaystyle \sum_{k \mathop = 1}^{99} k = \dfrac {99 \times \paren {99 + 1} } 2$


 * The $50$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $3160$, $3321$, $3486$, $3655$, $3828$, $4005$, $4186$, $4371$, $4560$:
 * $4950 = \displaystyle \sum_{k \mathop = 1}^{50} \paren {4 k - 3} = 50 \paren {2 \times 50 - 1}$


 * The $6$th hexamorphic number after $1$, $45$, $66$, $1225$, $1326$:
 * $4950 = H_{50}$


 * The $12$th Kaprekar number after $1$, $9$, $45$, $55$, $99$, $297$, $703$, $999$, $2223$, $2728$, $4879$:
 * $4950^2 = 24 \, 502 \, 500 \to 2450 + 2500 = 4950$