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  • one year ago

Does this infinite series have a closed form?

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  1. Empty
    • one year ago
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    \[ \sum_{i=1}^{\infty} \frac{1}{p_i^{p_i}} \] Where \(p_i\) is the ith prime.

  2. Empty
    • one year ago
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    It appears to approach this since the terms die off really quickly: \[S \approx 0.287358...\] Does that resemble anything you've seen before? All I can say is it's slightly larger than e/10. Hahaha. http://www.wolframalpha.com/input/?i=1%2F2%5E2%2B1%2F3%5E3%2B1%2F5%5E5%2B...&t=crmtb01

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    • one year ago
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    Turns out base e and base 10 are more related than we thought? Ok probably not haha.

  4. ganeshie8
    • one year ago
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    https://oeis.org/A094289

  5. ganeshie8
    • one year ago
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    looks there isn't much online on this series

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