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$1/(2+1/(3+1/(5+...) = [0; 2,3,5,...p_{\infty}] \approx 0.432332$

Does this constant have a name? What is it called? It does appear to converge from my initial calculations, and I'm surprised that I can't easily find anything for the infinite continued fraction of the primes.

J. W. Tanner
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O.S.
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  • Possible duplicate: Continued fraction involving Fibonacci sequence – Cameron L. Williams Oct 01 '21 at 00:18
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    I think the numbers OP is referencing are primes, not Fibonacci numbers, based on the $p_\infty$ – PrincessEev Oct 01 '21 at 00:18
  • Your question is unclear. What is the sequence? primes? Fibonacci numbers? something else entirely? Why do you expect that it should have a name? What motivates the question? – Xander Henderson Oct 01 '21 at 00:21
  • You can find some connection about the constant there. https://oeis.org/A063083 – DuFong Oct 01 '21 at 00:17
  • Yes, it is the primes. I thought the $p_{\infty}$ communicated that but I have clarified it in the edit. I'm honestly surprised that I can't find much of anything regarding it – O.S. Oct 01 '21 at 00:25
  • and wouldn’t the Fibonacci sequence have $1$s before $2,3,5,...$? – J. W. Tanner Oct 01 '21 at 00:30
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    https://math.stackexchange.com/questions/63865/a-continued-fraction-involving-prime-numbers – Xander Henderson Oct 01 '21 at 00:31
  • While the proposed duplicate question is certainly related, it seems clear to me that this question is asking (in the title and in the body) for a name for the constant, while the proposed duplicate is asking for its value – J. W. Tanner Oct 01 '21 at 04:24
  • Is it known whether this number is transcendental ? – Peter Oct 01 '21 at 08:38
  • @J.W.Tanner Generally speaking, "What is [x] called?" is not a good question for Math SE, unless the asker can suggest a good reason why they believe that an object ought to have been named. I also believe that the linked question answers this question, as one would imagine that if some constant has a commonly used appellation, then the paper on arXiv would likely refer to such a designation. While it is hard to prove a negative, the linked Q&A seems to address the question here by implication. – Xander Henderson Oct 01 '21 at 14:20

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