51

Number
$51$ (fifty-one) is:


 * $3 \times 17$


 * The $3$rd term of the $1$st $5$-tuple of consecutive integers have the property that they are not values of the $\sigma$ function $\map \sigma n$ for any $n$:
 * $\tuple {49, 50, 51, 52, 53}$


 * The $6$th pentagonal number after $1$, $5$, $12$, $22$, $35$:
 * $51 = 1 + 4 + 7 + 10 + 13 + 16 = \dfrac {6 \paren {3 \times 6 - 1} } 2$


 * The $9$th trimorphic number after $1$, $4$, $5$, $6$, $9$, $24$, $25$, $49$:
 * $51^3 = 132 \, 6 \mathbf {51}$


 * The $11$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$, $26$, $35$, $40$:
 * $51 = \dfrac {6 \paren {3 \times 6 - 1} } 2$


 * The $14$th lucky number:
 * $1$, $3$, $7$, $9$, $13$, $15$, $21$, $25$, $31$, $33$, $37$, $43$, $49$, $51$, $\ldots$


 * The $18$th semiprime after $4$, $6$, $9$, $10$, $14$, $15$, $21$, $22$, $25$, $26$, $33$, $34$, $35$, $38$, $39$, $46$, $49$:
 * $51 = 3 \times 17$


 * The $19$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
 * $3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $40$, $43$, $48$, $51$, $\ldots$


 * The $23$rd after $1$, $2$, $4$, $5$, $6$, $8$, $9$, $12$, $13$, $15$, $16$, $17$, $20$, $24$, $25$, $27$, $28$, $32$, $35$, $26$, $39$, $48$ of the $24$ positive integers which cannot be expressed as the sum of distinct non-pythagorean primes.


 * The $30$th integer $n$ such that $2^n$ contains no zero in its decimal representation:
 * $2^{51} = 2 \, 251 \, 799 \, 813 \, 685 \, 248$


 * Suggested by in his $1997$ book  as being the smallest uninteresting number, which fact makes it intrinsically interesting.

Also see

 * Interesting Number Paradox