484

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Number

$484$ (four hundred and eighty-four) is:

$2^2 \times 11^2$

The $1$st of the only $3$ square numbers which start and end with $n$ $4$s.

The $10$th integer after $0$, $1$, $2$, $4$, $8$, $121$, $151$, $212$, $242$ which is palindromic in both decimal and ternary:

$484_{10} = 122 \, 221_3$

The $14$th square after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$, $121$, $144$, $225$, $441$ which has no more than $2$ distinct digits and does not end in $0$:

$484 = 22^2$

The $22$nd square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $225$, $256$, $289$, $324$, $361$, $400$, $441$:

$484 = 22 \times 22$

The $37$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $\ldots$, $289$, $324$, $343$, $361$, $392$, $400$, $432$, $441$:

$484 = 2^2 \times 11^2$

The palindromic square of the palindromic number $22$:

$22^2 = 484$

Also see

• Square of Small-Digit Palindromic Number is Palindromic

• Previous  ... Next: Palindromes in Base 10 and Base 3

• Previous  ... Next: Powerful Number
• Previous  ... Next: Square Number
• Previous  ... Next: Squares with No More than 2 Distinct Digits

• Next: Sequence of Squares Beginning and Ending with n 4s

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $484$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $484$