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$2$ is the $1$st prime.

$3$ is the $2$nd prime.

$5$ is the $3$rd prime.

$11$ is the $5$th prime.

$31$ is the $11$th prime.

...

I'm just wondering if there is a name for this integer sequence, is it on OEIS?. I find it hard to find a suitable search term for it.

Auberon
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    https://oeis.org/search?q=3%2C5%2C11%2C31&sort=&language=&go=Search – Ethan Bolker Nov 18 '17 at 19:20
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    I'd imagine there is no name nor search term for it because it's absolutely meaningless, both theoretically and practically. –  Nov 18 '17 at 19:20
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    The formula is $\large p_{p_n}$, but I never heard a name for it. And why is this theoretically meaningless ? I once asked whether the sum of the reciprocals of those numbers converges. It is a quite natural next step. We have the primes, and then, we only consider primes $p_n$ , for which the index $n$ is prime. But how should we call those numbers ? Does anyone have a good idea ? – Peter Nov 18 '17 at 19:44
  • @Peter. By the prime number theorem $p_n \sim n \log n$ thus $$\sum_n \frac{1}{p_{p_n}} \le C\sum_n \frac{1}{p_n\log p_n} \le C_2 \sum_n \frac{1}{(n\log n) \log( n\log n)} \le C_3 \sum_n \frac{1}{n \log^2 n} < \infty$$ You can create thousands of such meaningless and useless functions/sequences in number theory. In the same way there is no name for the antiderivative of $\frac{\exp(\sin(x^{1/2}))}{\tan x}$. – reuns Nov 18 '17 at 19:48
  • https://oeis.org/search?q=3%2C5%2C11%2C17%2C31&language=english&go=Search https://www.wolframalpha.com/input/?i=table%5BPrimeN%5BPrimeN%5Bn%5D%5D,%7Bn,1,10%7D%5D – reuns Nov 18 '17 at 19:54
  • OEIS would be a good thing, if they would stop the annoying donation appeal. You enter a sequence, scroll down and you are thrown back to the top , so you are forced to notice the appeal. Unfortunately, a successful strategy, but really annoying. Wikipedia is worse because the appeal scrolls down if you scroll down, so you cannot escape at all the appeal. It is sad that so much money can be made with such methods. – Peter Nov 18 '17 at 22:00

1 Answers1

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The numbers in your sequence form OEIS A007097, i.e., the recurrence denoted by $a(n)$ such that:

$$ a(n+1) = a(n)^{\rm th} \rm \ \ prime. $$

This is called the primeth recurrence.

Klangen
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