2145
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Number
$2145$ (two thousand, one hundred and forty-five) is:
- $3 \times 5 \times 11 \times 13$
- The $1$st of the $6$th pair of triangular numbers whose sum and difference are also both triangular:
- $2145 = T_{65}$, $3741 = T_{86}$, $3741 + 2145 = T_{108}$, $3741 - 2145 = T_{56}$
- The $33$rd hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $703$, $780$, $861$, $946$, $1035$, $1225$, $1326$, $1431$, $1540$, $1653$, $1770$, $1891$, $2016$:
- $2145 = \ds \sum_{k \mathop = 1}^{33} \paren {4 k - 3} = 33 \paren {2 \times 33 - 1}$
- The $65$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $1326$, $1378$, $1431$, $1485$, $1540$, $1596$, $1653$, $1711$, $1770$, $1770$, $1830$, $1891$, $1953$, $2016$, $2080$:
- $2145 = \ds \sum_{k \mathop = 1}^{65} k = \dfrac {65 \times \paren {65 + 1} } 2$