# 5778

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## Number

$5778$ (five thousand, seven hundred and seventy-eight) is:

$2 \times 3^3 \times 107$

The $3$rd and last Lucas number after $1$, $3$ which is also triangular:
$5778 = \displaystyle \sum_{k \mathop = 1}^{107} k = \dfrac {107 \times \paren {107 + 1} } 2 = 2207 + 3571$

The $18$th Lucas number after $(2)$, $1$, $3$, $4$, $7$, $11$, $18$, $29$, $47$, $76$, $123$, $199$, $322$, $521$, $843$, $1364$, $2207$, $3571$:
$5778 = 2207 + 3571$

The $54$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $4005$, $4186$, $4371$, $4560$, $4950$, $5151$, $5356$, $5565$:
$5778 = \displaystyle \sum_{k \mathop = 1}^{54} \paren {4 k - 3} = 54 \paren {2 \times 54 - 1}$

The $107$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $5253$, $5356$, $5460$, $5565$, $5671$:
$5778 = \displaystyle \sum_{k \mathop = 1}^{107} k = \dfrac {107 \times \paren {107 + 1} } 2$