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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
2 years, 10 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 \(s(n) = \sigma(n) - n\))

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

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

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

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

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

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

\((\Sigma(3))! = 24\) Samuraiwarm Tsunayoshi · 2 years, 10 months ago

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@Samuraiwarm Tsunayoshi 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 Samuraiwarm Tsunayoshi · 2 years, 10 months ago

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

so credits goes to Kenny Lau and Vinay Sipani Deepak Gowda · 2 years, 10 months ago

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@Deepak Gowda Ty... But the credit must go to you.. Vinay Sipani · 2 years, 10 months ago

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  • \(\left\lfloor{cotan(3°)}\right\rfloor=20\)
  • \(\left\lceil{cotan(3°)}\right\rceil=19\)
  • \(\mu(\mu(3))=1\)
  • \(\frac{d}{dx}(3)=0\)
  • σ(3)=4 where σ(n) is sum of positive divisors.
Vinay Sipani · 2 years, 10 months ago

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@Vinay Sipani Well, \(\frac d{dx}(3)=0\). Kenny Lau · 2 years, 10 months ago

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@Kenny Lau oops yeah...its 0 mis-typo... Vinay Sipani · 2 years, 10 months ago

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@Vinay Sipani The floor and ceiling is also switched too. Samuraiwarm Tsunayoshi · 2 years, 10 months ago

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