The nth prime where n is prime. [duplicate]
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This question already has an answer here:
Prime numbers the rank of which is also a prime.
2 answers
$2$ 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.
prime-numbers terminology
asked Nov 18 '17 at 19:16
Auberon
277112
marked as duplicate by user10354138, José Carlos Santos, rtybase, amWhy, Lord_Farin Nov 28 at 19:22
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
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show 1 more comment
up vote
1
down vote
favorite
This question already has an answer here:
Prime numbers the rank of which is also a prime.
2 answers
$2$ 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.
prime-numbers terminology
asked Nov 18 '17 at 19:16
Auberon
277112
marked as duplicate by user10354138, José Carlos Santos, rtybase, amWhy, Lord_Farin Nov 28 at 19:22
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
1
oeis.org/…
– Ethan Bolker
Nov 18 '17 at 19:20
2
I'd imagine there is no name nor search term for it because it's absolutely meaningless, both theoretically and practically.
– Professor Vector
Nov 18 '17 at 19:20
1
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 $$sum_n frac{1}{p_{p_n}} le Csum_n frac{1}{p_nlog p_n} le C_2 sum_n frac{1}{(nlog n) log( nlog n)} le C_3 sum_n frac{1}{n log^2 n} < infty$$ 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
oeis.org/… wolframalpha.com/input/…
– reuns
Nov 18 '17 at 19:54
|
show 1 more comment
up vote
1
down vote
favorite
up vote
1
down vote
favorite
This question already has an answer here:
Prime numbers the rank of which is also a prime.
2 answers
$2$ 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.
prime-numbers terminology
asked Nov 18 '17 at 19:16
Auberon
277112
This question already has an answer here:
Prime numbers the rank of which is also a prime.
2 answers
$2$ 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.
This question already has an answer here:
Prime numbers the rank of which is also a prime.
2 answers
prime-numbers terminology
prime-numbers terminology
asked Nov 18 '17 at 19:16
Auberon
277112
asked Nov 18 '17 at 19:16
Auberon
277112
edited Nov 18 '17 at 19:30
asked Nov 18 '17 at 19:16
Auberon
277112
asked Nov 18 '17 at 19:16
Auberon
277112
asked Nov 18 '17 at 19:16
Auberon
277112
277112
marked as duplicate by user10354138, José Carlos Santos, rtybase, amWhy, Lord_Farin Nov 28 at 19:22
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by user10354138, José Carlos Santos, rtybase, amWhy, Lord_Farin Nov 28 at 19:22
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
1
oeis.org/…
– Ethan Bolker
Nov 18 '17 at 19:20
2
I'd imagine there is no name nor search term for it because it's absolutely meaningless, both theoretically and practically.
– Professor Vector
Nov 18 '17 at 19:20
1
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 $$sum_n frac{1}{p_{p_n}} le Csum_n frac{1}{p_nlog p_n} le C_2 sum_n frac{1}{(nlog n) log( nlog n)} le C_3 sum_n frac{1}{n log^2 n} < infty$$ 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
oeis.org/… wolframalpha.com/input/…
– reuns
Nov 18 '17 at 19:54
|
show 1 more comment
1
oeis.org/…
– Ethan Bolker
Nov 18 '17 at 19:20
2
I'd imagine there is no name nor search term for it because it's absolutely meaningless, both theoretically and practically.
– Professor Vector
Nov 18 '17 at 19:20
1
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 $$sum_n frac{1}{p_{p_n}} le Csum_n frac{1}{p_nlog p_n} le C_2 sum_n frac{1}{(nlog n) log( nlog n)} le C_3 sum_n frac{1}{n log^2 n} < infty$$ 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
oeis.org/… wolframalpha.com/input/…
– reuns
Nov 18 '17 at 19:54
1
1
oeis.org/…
– Ethan Bolker
Nov 18 '17 at 19:20
oeis.org/…
– Ethan Bolker
Nov 18 '17 at 19:20
2
2
I'd imagine there is no name nor search term for it because it's absolutely meaningless, both theoretically and practically.
– Professor Vector
Nov 18 '17 at 19:20
I'd imagine there is no name nor search term for it because it's absolutely meaningless, both theoretically and practically.
– Professor Vector
Nov 18 '17 at 19:20
1
1
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
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 $$sum_n frac{1}{p_{p_n}} le Csum_n frac{1}{p_nlog p_n} le C_2 sum_n frac{1}{(nlog n) log( nlog n)} le C_3 sum_n frac{1}{n log^2 n} < infty$$ 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
@Peter. By the prime number theorem $p_n sim n log n$ thus $$sum_n frac{1}{p_{p_n}} le Csum_n frac{1}{p_nlog p_n} le C_2 sum_n frac{1}{(nlog n) log( nlog n)} le C_3 sum_n frac{1}{n log^2 n} < infty$$ 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
oeis.org/… wolframalpha.com/input/…
– reuns
Nov 18 '17 at 19:54
oeis.org/… wolframalpha.com/input/…
– reuns
Nov 18 '17 at 19:54
|
show 1 more comment
1 Answer
1
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up vote
1
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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.
answered Nov 21 at 12:48
Klangen
1,50811332
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
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.
answered Nov 21 at 12:48
Klangen
1,50811332
add a comment |
up vote
1
down vote
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.
answered Nov 21 at 12:48
Klangen
1,50811332
add a comment |
up vote
1
down vote
up vote
1
down vote
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.
answered Nov 21 at 12:48
Klangen
1,50811332
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.
answered Nov 21 at 12:48
Klangen
1,50811332
answered Nov 21 at 12:48
Klangen
1,50811332
answered Nov 21 at 12:48
Klangen
1,50811332
answered Nov 21 at 12:48
Klangen
1,50811332
1,50811332
add a comment |
add a comment |
1
oeis.org/…
– Ethan Bolker
Nov 18 '17 at 19:20
2
I'd imagine there is no name nor search term for it because it's absolutely meaningless, both theoretically and practically.
– Professor Vector
Nov 18 '17 at 19:20
1
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 $$sum_n frac{1}{p_{p_n}} le Csum_n frac{1}{p_nlog p_n} le C_2 sum_n frac{1}{(nlog n) log( nlog n)} le C_3 sum_n frac{1}{n log^2 n} < infty$$ 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
oeis.org/… wolframalpha.com/input/…
– reuns
Nov 18 '17 at 19:54