A New Years Puzzle

[Alonso Del Arte]

I'm a college student, and I have no idea what the sequence

5,62,233,1444,8278,27778,76225,103872,184827,328473,399473,539283,...

is. I've tried looking up two terms at a time on the OEIS. "5, 62"
gives quite a few results. "62, 233" gives just two results, but one
of those is this very puzzle sequence.

Next, I turned to Wikipedia. It has a lot to say about the number 5,
but not much about the other numbers.

62 nontotient, atomic number of samarium, IDD code for Indonesia,
number of French department Pas-de-Calais
233 prime, Fibonacci number, Sophie Germain prime, self number
1444 = 38^2

Nothing about the numbers after that.

About the only thing I can rule out is its being a prime subset of
another sequence. It is possible that this sequence might be one of
those "primes of the form" sequences, but I have no idea what kind of
formula would give primes for these values but not for other values.

Should we be looking outside of mathematics for an answer? I
considered for a brief moment that it could be a sequence like 21, 36,
55, 60, 67, 68, 92, 93, 125, A001491, the opus numbers of Beethoven's
Symphonies. But the puzzle sequence gets too large too quickly,
requiring an impossibly prolific composer who only occasionally wrote
Symphonies.

I am thoroughly stumped by this sequence.

Alonso



On Mon, 3 Jan 2005 13:37:08 -0500 (EST), N. J. A. Sloane
<njas at research.att.com> wrote:
> 
> Dear Seqfans, A correspondent writes:
> 
> > From mbimmler at bluemail.ch  Mon Jan  3 07:31:50 2005
> > Date: Mon, 3 Jan 2005 13:31:14 +0100
> > From: "Michael Bimmler" <mbimmler at bluemail.ch>
> >
> > You must have this sequence in your database. It's a very basic one, even
> > a college student should know it...
> > 5,62,233,1444,8278,27778,76225,103872,184827,328473,399473,539283,...
> 
> Any ideas, anyone?  I didn't study it much.
> I asked him for an explanation, but got no reply.
> 
> I also have to say that I'm going to be really busy
> with the new book for the next few months, so
> it may take longer to process comments and new sequences
> than usual.    Happy New Year!   Neil
> 
>