111

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Number

$111$ (one hundred and eleven) is:

$3 \times 37$

The magic constant of the smallest prime magic square.

The $3$rd repuint after $1$, $11$

The $4$th of the $17$ positive integers for which the value of the Euler $\phi$ function is $72$:

$73$, $91$, $95$, $111$, $117$, $135$, $146$, $148$, $152$, $182$, $190$, $216$, $222$, $228$, $234$, $252$, $270$

The $6$th positive integer after $1$, $2$, $7$, $11$, $101$ whose cube is palindromic:

$111^3 = 1 \, 367 \, 631$

The magic constant of a magic square of order $6$, after $1$, $(5)$, $15$, $34$, $65$:

$111 = \ds \dfrac 1 6 \sum_{k \mathop = 1}^{6^2} k = \dfrac {6 \paren {6^2 + 1} } 2$

The $7$th palindromic lucky number:

$1$, $3$, $7$, $9$, $33$, $99$, $111$, $\ldots$

The $8$th palindromic integer after $0$, $1$, $2$, $3$, $11$, $22$, $101$ whose square is also palindromic integer

$111^2 = 12 \, 321$

The $15$th Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $15$, $24$, $36$:

$111 = 111 \times 1 = 111 \times \paren {1 \times 1 \times 1}$

The $24$th lucky number:

$1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $43$, $49$, $51$, $63$, $67$, $73$, $75$, $79$, $87$, $93$, $99$, $105$, $111$, $\ldots$

The $35$th semiprime:

$111 = 3 \times 37$

Also see

• Magic Constant of Smallest Prime Magic Square

• Previous  ... Next: Repunit
• Previous  ... Next: Zuckerman Number
• Previous  ... Next: Magic Constant of Magic Square
• Previous  ... Next: Numbers with Euler Phi Value of 72
• Previous  ... Next: Sequence of Palindromic Lucky Numbers
• Previous  ... Next: Square of Small-Digit Palindromic Number is Palindromic
• Previous  ... Next: Sequence of Integers whose Cube is Palindromic
• Previous  ... Next: Lucky Number
• Previous  ... Next: Semiprime Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $111$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $111$