# 1035

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## Number

$1035$ (one thousand and thirty-five) is:

$3^2 \times 5 \times 23$

The $23$rd hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $703$, $780$, $861$, $946$:
$1035 = \ds \sum_{k \mathop = 1}^{23} \paren {4 k - 3} = 23 \paren {2 \times 23 - 1}$

The $45$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $496$, $528$, $561$, $595$, $630$, $666$, $703$, $741$, $780$, $820$, $861$, $903$, $946$, $990$:
$1035 = \ds \sum_{k \mathop = 1}^{45} k = \dfrac {45 \times \paren {45 + 1} } 2$