# phi(phi(floor(exp(3!))))=96

This note's credits goes to a comment by Deepak Gowda in this post.

Generate 0 to 100 with only one digit once: the digit 3. You may use any other functions, like the one in the title.

Please enter as much as you can! :) Note by Kenny Lau
5 years, 6 months ago

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$\lfloor \sin(3^{\circ})\rfloor = 0$

$\text{sgn}(3) = 1$ (sign function)

$\phi(3) = 2$ (Euler's totient phi function)

$3$

$\sigma(3) = 4$ (divisor sum)

$\Sigma(3) = 5$ (prime sum)

$3! = 6$

$\lfloor \csc(3)\rfloor = 7$

$\lceil \csc(3)\rceil = 8$

$\lfloor\text{antilog}(\tan(3)) \rfloor = 9$ ($\text{antilog}(x) = 10^{x}$)

$\Sigma(\Sigma(3)) = 10$

$p_{\Sigma(3)} = 11$ (n-th prime number)

$\sigma(3!) = 12$

$F_{\lceil \csc(3)\rceil} = 13$ (Fibonacci function $F_{1} = 0, F_{2} = 1, F_{n+2} = F_{n} + F_{n+1}$)

$\sigma(F_{\lceil \csc(3)\rceil}) = 14$

$\sigma(\lceil \csc(3)\rceil) = 15$

$\phi(s(\sigma(\sigma(\sigma(3))))) = 16$

$s(\sigma(\sigma(\sigma(3)))) = 17$ (aliquot sum $s(n) = \sigma(n) - n$)

$\sigma(s(\sigma(\sigma(\sigma(3))))) = 18$

$p_{\lceil \csc(3)\rceil} = 19$

$\sigma(p_{\lceil \csc(3)\rceil}) = 20$

$\lfloor \tan(\tan(\cos(\sin(3^{\circ})))) \rfloor = 21$

$\lceil \tan(\tan(\cos(\sin(3^{\circ})))) \rceil = 22$

$p_{\lfloor\text{antilog}(\tan(3)) \rfloor} = 23$

$(\Sigma(3))! = 24$

- 5 years, 6 months ago

Actually we can do any prime numbers if we have first 25 numbers. And also prime numbers minus 1 using Euler's totient function. And also Fibonacci numbers. And also Lucas numbers. And blahuhuhuh

- 5 years, 6 months ago

• $\left\lfloor{cotan(3°)}\right\rfloor=20$
• $\left\lceil{cotan(3°)}\right\rceil=19$
• $\mu(\mu(3))=1$
• $\frac{d}{dx}(3)=0$
• σ(3)=4 where σ(n) is sum of positive divisors.

- 5 years, 6 months ago

Well, $\frac d{dx}(3)=0$.

- 5 years, 6 months ago

oops yeah...its 0 mis-typo...

- 5 years, 6 months ago

The floor and ceiling is also switched too.

- 5 years, 6 months ago

I've commented but you've created...

so credits goes to Kenny Lau and Vinay Sipani

- 5 years, 6 months ago

Ty... But the credit must go to you..

- 5 years, 6 months ago