1681

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Number

$1681$ (one thousand six hundred and eighty-one) is:

$41^2$

The $6$th square after $49$, $169$, $361$, $1225$, $1444$ whose decimal representation can be split into two parts which are each themselves square:

$1681 = 41^2$; $16 = 4^2$, $81 = 9^2$

and the only such number of $4$ digits whose two parts are both of $2$ digits

The $36$th positive integer which cannot be expressed as the sum of a square and a prime:

$1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $706$, $730$, $771$, $784$, $841$, $1024$, $1089$, $1225$, $1255$, $1351$, $1414$, $1444$, $1521$, $1681$, $\ldots$

The $41$st square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $1024$, $1089$, $1156$, $1225$, $1296$, $1369$, $1444$, $1521$, $1600$:

$1681 = 41 \times 41$

Also see

• Previous  ... Next: Squares whose Digits can be Separated into 2 other Squares
• Previous  ... Next: Numbers not Sum of Square and Prime
• Previous  ... Next: Square Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1681$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1681$