1111

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Number

$1111$ (one thousand, one hundred and eleven) is:

$11 \times 101$

The $4$th repuint after $1$, $11$, $111$

The $8$th palindromic integer after $0$, $1$, $2$, $3$, $11$, $77$, $363$ which is the index of a palindromic triangular number

$T_{1111} = 617 \, 716$

The $13$th palindromic integer after $0$, $1$, $2$, $3$, $11$, $22$, $101$, $111$, $121$, $202$, $212$, $1001$ whose square is also palindromic integer

$1111^2 = 1 \, 234 \, 321$

The $35$th Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $\ldots$, $216$, $224$, $312$, $315$, $384$, $432$, $612$, $624$, $672$, $735$, $816$:

$1111 = 1111 \times 1 = 1111 \times \paren {1 \times 1 \times 1 \times 1}$

The $51$st Smith number after $4$, $22$, $27$, $58$, $\ldots$, $778$, $825$, $852$, $895$, $913$, $915$, $922$, $958$, $985$, $1086$:

$1 + 1 + 1 + 1 = 1 + 1 + 1 + 0 + 1 = 4$

$1111 = 56^2 - 45^2$

Also see

• Difference between Two Squares equal to Repunit

• Previous  ... Next: Repunit
• Previous  ... Next: Palindromic Indices of Palindromic Triangular Numbers
• Previous  ... Next: Zuckerman Number
• Previous  ... Next: Square of Small-Digit Palindromic Number is Palindromic
• Previous  ... Next: Smith Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1111$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1111$