495
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Number
$495$ (four hundred and ninety-five) is:
- $3^2 \times 5 \times 11$
- The $9$th pentatope number after $1$, $5$, $15$, $35$, $70$, $126$, $210$, $330$:
- $495 = \ds \sum_{k \mathop = 1}^9 \dfrac {k \paren {k + 1} \paren {k + 2} } 6 = \dfrac {9 \paren {9 + 1} \paren {9 + 2} \paren {9 + 3} } {24}$
- The $18$th second pentagonal number after $2$, $7$, $15$, $26$, $40$, $57$, $77$, $100$, $126$, $155$, $187$, $222$, $260$, $301$, $345$, $392$, $442$:
- $495 = \dfrac {18 \paren {3 \times 18 + 1} } 2$
- The $36$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $222$, $247$, $260$, $287$, $301$, $330$, $345$, $376$, $392$, $425$, $442$, $477$:
- $495 = \dfrac {18 \paren {3 \times 18 + 1} } 2$
- Kaprekar's process, when applied to a $3$-digit integer whose digits are not all the same, results in $495$ after no more than $6$ iterations.
Also see
- Previous ... Next: Pentatope Number
- Previous ... Next: Second Pentagonal Number
- Previous ... Next: Generalized Pentagonal Number
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $495$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $495$