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Are there infinitely many insipid numbers? Are There Primes of Every Hamming Weight?Central numbers and de Polignac's conjectureDoes the hyperoctahedral group have only 3 maximal normal subgroups?Are the distributive permutation groups linearly primitive?Are the finite groups inclusions, almost all relatively cyclic?Large subgroups of $S_n$ without large symmetric or alternating subgroupsWhen does the first subgroup growth function grow?Is there a subgroup of dual depth 3?Existence of infinitely many number fields with bounded class numberThe sporadic numbers 2 1 $begingroup$ 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:

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