How do I make a function that generates nth natural number that isn't a perfect square?Convergent subsequencesHow to find a “better description” (e.g. recurrence relation) for this sequence?Determine the value for which a sequence is an arithmetic progression.Convergence of a sequence in a Hilbert space2-cycles and limitsFind a recursive definition for the sequencesMonotonicity of $fracnsqrt[n](n!)$$2021^textst$ term of a SequenceGetting a specific element of a non-recursive sequenceHow to calculate the general formula for nth term of this recursion?
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How do I make a function that generates nth natural number that isn't a perfect square?
Convergent subsequencesHow to find a “better description” (e.g. recurrence relation) for this sequence?Determine the value for which a sequence is an arithmetic progression.Convergence of a sequence in a Hilbert space2-cycles and limitsFind a recursive definition for the sequencesMonotonicity of $fracnsqrt[n](n!)$$2021^textst$ term of a SequenceGetting a specific element of a non-recursive sequenceHow to calculate the general formula for nth term of this recursion?
$begingroup$
So I want to make a function such that for every n that you input it generates nth natural number that isn't a perfect square, like 2, 3, 5,...? I tried recurrance relation and I can't seem to find the proper relation between the members of sequence. Then I tried making a function but I don't know what to use actually... Any help?
sequences-and-series roots
asked 3 hours ago
Adnan CAdnan C
335
$endgroup$
add a comment |
$begingroup$
So I want to make a function such that for every n that you input it generates nth natural number that isn't a perfect square, like 2, 3, 5,...? I tried recurrance relation and I can't seem to find the proper relation between the members of sequence. Then I tried making a function but I don't know what to use actually... Any help?
sequences-and-series roots
asked 3 hours ago
Adnan CAdnan C
335
$endgroup$
add a comment |
$begingroup$
So I want to make a function such that for every n that you input it generates nth natural number that isn't a perfect square, like 2, 3, 5,...? I tried recurrance relation and I can't seem to find the proper relation between the members of sequence. Then I tried making a function but I don't know what to use actually... Any help?
sequences-and-series roots
asked 3 hours ago
Adnan CAdnan C
335
$endgroup$
So I want to make a function such that for every n that you input it generates nth natural number that isn't a perfect square, like 2, 3, 5,...? I tried recurrance relation and I can't seem to find the proper relation between the members of sequence. Then I tried making a function but I don't know what to use actually... Any help?
sequences-and-series roots
sequences-and-series roots
asked 3 hours ago
Adnan CAdnan C
335
asked 3 hours ago
Adnan CAdnan C
335
asked 3 hours ago
Adnan CAdnan C
335
asked 3 hours ago
Adnan CAdnan C
335
asked 3 hours ago
Adnan CAdnan C
335
335
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
OEIS to the rescue.
It gives the formula
$$
n+leftlfloorfrac12+sqrt nrightrfloor.
$$
where $lfloorcdotrfloor$ is the floor function.
answered 3 hours ago
ArthurArthur
124k7122211
$endgroup$
add a comment |
$begingroup$
Let $Bbb N = 1,2,3,dots$.
Let $pi_1$ and $pi_2$ be the two coordinate projection mappings on $Bbb N times Bbb N$.
We will define a function $f$ using recursion.
Define $f(1) = (2,2)$.
For $n ge 1$ define
$$
f(n+1) = leftbeginarraylr
left ( , pi_1(f(n)) + 1 ,pi_2(f(n)), right ) & textwhen pi_1(f(n)) + 1 lt [pi_2(f(n))]^2 \
left ( , pi_1(f(n)) + 2 ,pi_2(f(n))+1 , right ) & textelse
endarrayright
$$
The function $pi_1 circ f$ has the desired properties.
answered 1 hour ago
CopyPasteItCopyPasteIt
4,4471828
$endgroup$
add a comment |
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2 Answers
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active
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2 Answers
2
active
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$begingroup$
OEIS to the rescue.
It gives the formula
$$
n+leftlfloorfrac12+sqrt nrightrfloor.
$$
where $lfloorcdotrfloor$ is the floor function.
answered 3 hours ago
ArthurArthur
124k7122211
$endgroup$
add a comment |
$begingroup$
OEIS to the rescue.
It gives the formula
$$
n+leftlfloorfrac12+sqrt nrightrfloor.
$$
where $lfloorcdotrfloor$ is the floor function.
answered 3 hours ago
ArthurArthur
124k7122211
$endgroup$
add a comment |
$begingroup$
OEIS to the rescue.
It gives the formula
$$
n+leftlfloorfrac12+sqrt nrightrfloor.
$$
where $lfloorcdotrfloor$ is the floor function.
answered 3 hours ago
ArthurArthur
124k7122211
$endgroup$
OEIS to the rescue.
It gives the formula
$$
n+leftlfloorfrac12+sqrt nrightrfloor.
$$
where $lfloorcdotrfloor$ is the floor function.
answered 3 hours ago
ArthurArthur
124k7122211
answered 3 hours ago
ArthurArthur
124k7122211
answered 3 hours ago
ArthurArthur
124k7122211
answered 3 hours ago
ArthurArthur
124k7122211
124k7122211
add a comment |
add a comment |
$begingroup$
Let $Bbb N = 1,2,3,dots$.
Let $pi_1$ and $pi_2$ be the two coordinate projection mappings on $Bbb N times Bbb N$.
We will define a function $f$ using recursion.
Define $f(1) = (2,2)$.
For $n ge 1$ define
$$
f(n+1) = leftbeginarraylr
left ( , pi_1(f(n)) + 1 ,pi_2(f(n)), right ) & textwhen pi_1(f(n)) + 1 lt [pi_2(f(n))]^2 \
left ( , pi_1(f(n)) + 2 ,pi_2(f(n))+1 , right ) & textelse
endarrayright
$$
The function $pi_1 circ f$ has the desired properties.
answered 1 hour ago
CopyPasteItCopyPasteIt
4,4471828
$endgroup$
add a comment |
$begingroup$
Let $Bbb N = 1,2,3,dots$.
Let $pi_1$ and $pi_2$ be the two coordinate projection mappings on $Bbb N times Bbb N$.
We will define a function $f$ using recursion.
Define $f(1) = (2,2)$.
For $n ge 1$ define
$$
f(n+1) = leftbeginarraylr
left ( , pi_1(f(n)) + 1 ,pi_2(f(n)), right ) & textwhen pi_1(f(n)) + 1 lt [pi_2(f(n))]^2 \
left ( , pi_1(f(n)) + 2 ,pi_2(f(n))+1 , right ) & textelse
endarrayright
$$
The function $pi_1 circ f$ has the desired properties.
answered 1 hour ago
CopyPasteItCopyPasteIt
4,4471828
$endgroup$
add a comment |
$begingroup$
Let $Bbb N = 1,2,3,dots$.
Let $pi_1$ and $pi_2$ be the two coordinate projection mappings on $Bbb N times Bbb N$.
We will define a function $f$ using recursion.
Define $f(1) = (2,2)$.
For $n ge 1$ define
$$
f(n+1) = leftbeginarraylr
left ( , pi_1(f(n)) + 1 ,pi_2(f(n)), right ) & textwhen pi_1(f(n)) + 1 lt [pi_2(f(n))]^2 \
left ( , pi_1(f(n)) + 2 ,pi_2(f(n))+1 , right ) & textelse
endarrayright
$$
The function $pi_1 circ f$ has the desired properties.
answered 1 hour ago
CopyPasteItCopyPasteIt
4,4471828
$endgroup$
Let $Bbb N = 1,2,3,dots$.
Let $pi_1$ and $pi_2$ be the two coordinate projection mappings on $Bbb N times Bbb N$.
We will define a function $f$ using recursion.
Define $f(1) = (2,2)$.
For $n ge 1$ define
$$
f(n+1) = leftbeginarraylr
left ( , pi_1(f(n)) + 1 ,pi_2(f(n)), right ) & textwhen pi_1(f(n)) + 1 lt [pi_2(f(n))]^2 \
left ( , pi_1(f(n)) + 2 ,pi_2(f(n))+1 , right ) & textelse
endarrayright
$$
The function $pi_1 circ f$ has the desired properties.
answered 1 hour ago
CopyPasteItCopyPasteIt
4,4471828
edited 1 hour ago
answered 1 hour ago
CopyPasteItCopyPasteIt
4,4471828
answered 1 hour ago
CopyPasteItCopyPasteIt
4,4471828
answered 1 hour ago
CopyPasteItCopyPasteIt
4,4471828
4,4471828
add a comment |
add a comment |
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