Are there infinitely many insipid numbers?Are There Primes of Every Hamming Weight?Central numbers and de...
Are there infinitely many insipid numbers?
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$begingroup$
A number $n$ is called insipid if the groups having a core-free maximal subgroup of index $n$ are exactly $A_n$ and $S_n$. There is an OEIS enter for these numbers: A102842. There are exactly $486$ insipid numbers less than $1000$.
Question: Are there infinitely many insipid numbers?
Let $iota(r)$ be the number of insipid numbers less than $r$. The following plot (from OEIS) leads to:
Bonus question: Is it true that $lim_{r to infty}r/iota(r)=2$?
nt.number-theory gr.group-theory finite-groups permutation-groups oeis
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
$endgroup$
add a comment |
$begingroup$
A number $n$ is called insipid if the groups having a core-free maximal subgroup of index $n$ are exactly $A_n$ and $S_n$. There is an OEIS enter for these numbers: A102842. There are exactly $486$ insipid numbers less than $1000$.
Question: Are there infinitely many insipid numbers?
Let $iota(r)$ be the number of insipid numbers less than $r$. The following plot (from OEIS) leads to:
Bonus question: Is it true that $lim_{r to infty}r/iota(r)=2$?
nt.number-theory gr.group-theory finite-groups permutation-groups oeis
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
$endgroup$
add a comment |
$begingroup$
A number $n$ is called insipid if the groups having a core-free maximal subgroup of index $n$ are exactly $A_n$ and $S_n$. There is an OEIS enter for these numbers: A102842. There are exactly $486$ insipid numbers less than $1000$.
Question: Are there infinitely many insipid numbers?
Let $iota(r)$ be the number of insipid numbers less than $r$. The following plot (from OEIS) leads to:
Bonus question: Is it true that $lim_{r to infty}r/iota(r)=2$?
nt.number-theory gr.group-theory finite-groups permutation-groups oeis
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
$endgroup$
A number $n$ is called insipid if the groups having a core-free maximal subgroup of index $n$ are exactly $A_n$ and $S_n$. There is an OEIS enter for these numbers: A102842. There are exactly $486$ insipid numbers less than $1000$.
Question: Are there infinitely many insipid numbers?
Let $iota(r)$ be the number of insipid numbers less than $r$. The following plot (from OEIS) leads to:
Bonus question: Is it true that $lim_{r to infty}r/iota(r)=2$?
nt.number-theory gr.group-theory finite-groups permutation-groups oeis
nt.number-theory gr.group-theory finite-groups permutation-groups oeis
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
asked 8 hours ago
Sebastien PalcouxSebastien Palcoux
8,7884 gold badges40 silver badges110 bronze badges
8,7884 gold badges40 silver badges110 bronze badges
add a comment |
add a comment |
1 Answer
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$begingroup$
Almost all $n$ are insipid. In fact, the number of non-insipid numbers at most $n$ grows like $2n/log n$.
See "Cameron, Peter J.; Neumann, Peter M.; Teague, David N. On the degrees of primitive permutation groups. Math. Z. 180 (1982), 141–149."
answered 7 hours ago
verretverret
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1 Answer
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1 Answer
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$begingroup$
Almost all $n$ are insipid. In fact, the number of non-insipid numbers at most $n$ grows like $2n/log n$.
See "Cameron, Peter J.; Neumann, Peter M.; Teague, David N. On the degrees of primitive permutation groups. Math. Z. 180 (1982), 141–149."
answered 7 hours ago
verretverret
2,1171 gold badge13 silver badges24 bronze badges
$endgroup$
add a comment |
$begingroup$
Almost all $n$ are insipid. In fact, the number of non-insipid numbers at most $n$ grows like $2n/log n$.
See "Cameron, Peter J.; Neumann, Peter M.; Teague, David N. On the degrees of primitive permutation groups. Math. Z. 180 (1982), 141–149."
answered 7 hours ago
verretverret
2,1171 gold badge13 silver badges24 bronze badges
$endgroup$
add a comment |
$begingroup$
Almost all $n$ are insipid. In fact, the number of non-insipid numbers at most $n$ grows like $2n/log n$.
See "Cameron, Peter J.; Neumann, Peter M.; Teague, David N. On the degrees of primitive permutation groups. Math. Z. 180 (1982), 141–149."
answered 7 hours ago
verretverret
2,1171 gold badge13 silver badges24 bronze badges
$endgroup$
Almost all $n$ are insipid. In fact, the number of non-insipid numbers at most $n$ grows like $2n/log n$.
See "Cameron, Peter J.; Neumann, Peter M.; Teague, David N. On the degrees of primitive permutation groups. Math. Z. 180 (1982), 141–149."
answered 7 hours ago
verretverret
2,1171 gold badge13 silver badges24 bronze badges
answered 7 hours ago
verretverret
2,1171 gold badge13 silver badges24 bronze badges
answered 7 hours ago
verretverret
2,1171 gold badge13 silver badges24 bronze badges
answered 7 hours ago
verretverret
2,1171 gold badge13 silver badges24 bronze badges
2,1171 gold badge13 silver badges24 bronze badges
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