5151

Number
$5151$ (five thousand, one hundred and fifty-one) is:


 * $51 \times 101$


 * The $101$st triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $4560$, $4656$, $4753$, $4851$, $4950$, $5050$:
 * $5151 = \displaystyle \sum_{k \mathop = 1}^{101} k = \dfrac {101 \times \left({101 + 1}\right)} 2$


 * The $51$st hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $4005$, $4186$, $4371$, $4560$, $4950$:
 * $5151 = \displaystyle \sum_{k \mathop = 1}^{51} \left({4 k - 3}\right) = 51 \left({2 \times 51 - 1}\right)$


 * The $7$th hexamorphic number after $1$, $45$, $66$, $1225$, $1326$, $4950$:
 * $5151 = H_{51}$