1225
Jump to navigation
Jump to search
Number
$1225$ (one thousand, two hundred and twenty-five) is:
- $5^2 \times 7^2$
- The $2$nd square number after $1$ which can be expressed as the sum of a sequence of odd cubes from $1$:
- $1225 = 35^2 = 1^3 + 3^3 + 5^3 + 7^3 + 9^3$
- The $3$rd number after $1$, $36$ to be both square and triangular:
- $1225 = 35^2 = \dfrac {49 \times \paren {49 + 1} } 2$
- The $4$th hexamorphic number after $1$, $45$, $66$:
- $1225 = H_{25}$
- The $4$th square after $49$, $169$, $361$ whose decimal representation can be split into two parts which are each themselves square:
- $1225 = 35^2$; $1 = 1^2$, $225 = 15^2$
- The total of all the entries in a magic square of order $7$, after $1$, $(10)$, $45$, $136$, $325$, $666$:
- $1225 = \ds \sum_{k \mathop = 1}^{7^2} k = \dfrac {7^2 \paren {7^2 + 1} } 2$
- The $25$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $703$, $780$, $861$, $946$, $1035$, $1128$:
- $1225 = \ds \sum_{k \mathop = 1}^{25} \paren {4 k - 3} = 25 \paren {2 \times 25 - 1}$
- The $30$th positive integer which cannot be expressed as the sum of a square and a prime:
- $1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $706$, $730$, $771$, $784$, $841$, $1024$, $1089$, $1225$, $\ldots$
- The $35$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $625$, $676$, $729$, $784$, $841$, $900$, $961$, $1024$, $1089$, $1156$:
- $1225 = 35 \times 35$
- The $49$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $496$, $528$, $561$, $595$, $630$, $666$, $703$, $741$, $780$, $820$, $861$, $903$, $946$, $990$, $1035$, $1081$, $1128$, $1176$:
- $1225 = \ds \sum_{k \mathop = 1}^{49} k = \dfrac {49 \times \paren {49 + 1} } 2$
Also see
- Previous ... Next: Square Numbers which are Sum of Sequence of Odd Cubes
- Previous ... Next: Integer both Square and Triangular
- Previous ... Next: Hexamorphic Number
- Previous ... Next: Squares whose Digits can be Separated into 2 other Squares
- Previous ... Next: Sum of Terms of Magic Square
- Previous ... Next: Numbers not Sum of Square and Prime
- Previous ... Next: Hexagonal Number
- Previous ... Next: Square Number
- Previous ... Next: Triangular Number
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1225$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1225$