[seqfan] Re: Naming advice

[israel at math.ubc.ca]

I think clarity is better than catchiness, and I don't agree that "we don't
like to see sequence numbers in the names of other sequences". There are
lots of sequences with sequence numbers in their names. 
My suggestion would be
  a(n) is the unique k such that A108951(k) = n!.

Cheers,
Robert

On Mar 20 2019, Allan Wechsler wrote:

>I'm about to submit a sequence which I think is reasonably interesting, and
>the only thing that is holding me up is lack of a good name. I'm hoping you
>SeqFans can suggest something catchy.
>
>For background, A034385 are the "primorials", the product of all primes not
>exceeding N.
>
>A108951, which I will call F(N) here, is a kind of extension to the
>primorials. It agrees with A034385 when N is prime, and then uses the rule
>that F(AB) = F(A)F(B) when the argument is composite. For example, F(18) =
>F(2)F(3)F(3) = 2*6*6 = 72.
>
>Now, it's a theorem (proof left to the reader for brevity) that all
>ordinary factorials N! appear as F(K) for some K. My new sequence is
>"Unique K such that F(K) = N!". If nobody comes up with a helpful name, my
>fallback will have to be "Index of N! in A108951", but in general we don't
>like to see sequence numbers in the names of other sequences.
>
>What would really help is a good name for A108951(N). If F(N) were called
>the "blerp" of N (not suggesting that seriously!) then my new sequence
>would be the antiblerp of N factorial.
>
>Notice that the entries in A108951 are all the least exemplars of their
>prime signatures, so it is a permutation of A025487. These important
>numbers are listed in "number-theoretic" order in the former sequence, and
>in order of size in the latter.
>
>I welcome any ideas. There are actually a bunch of sequences waiting to be
>entered, based on the fact that a lot of sequences are subsets of A025487,
>and tend to be awkwardly large (like factorials) -- their "antiblerps" are
>usually much smaller and provide a sort of outline of the factorization of
>the original number.
>
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>
>