[seqfan] Re: 4775 and cretan numbers

[Olivier Gerard]

Neil wrote
>
> %T A033620 33,35,36,40,42,44,45,48,49,50,54,55,56,60
[...]
> %K A033620 nonn,base,more
> but 4775 won't appear there for a long time

in fact 4775 is the 594th term of this sequence.
Here are more terms:

%T A033620 33,35,36,40,42,44,45,48,49,50,54,55,56,60,63,64,66,70,72,75,77,80=
,
%U A033620 81,84,88,90,96,98,99,100,101,105,108,110,112,120,121,125,126,128,=
131

I do not agree completely with Neil's sentence:

> so 4775 is a candidate for the world's least interesting number

because as the property proposed by Jud shows, a number can very well
not be present in the database because it is a member of a sequence
which fills 3 lines before reaching it. On the other hand, an
interesting number has at least one or two more "select" properties
than say, being odd or even.

Another base dependent property of 4775 is of being a base 10 palindrom +1
and a base 17 palindrom -1

There are not many integers like that. Here are the first non trivial ones
(I mean, superior to 17):

%I A0xxxxx
%S A0xxxxx 89,233,374,425,596,647,869,920,3444,4775
%N A0xxxxx 1+ a base 10-palindrom and -1 + a base 17-palindrom
%R A0xxxxx
%O A0xxxxx 1,1
%K A0xxxxx nonn,base,more
%A A0xxxxx Olivier Gerard (ogerard at ext.jussieu.fr)
%C A0xxxxx From the famous contest "Including 4775 in the database".

the next term (if it exists) is superior to 10000.
but with properties of that kind one could distinguish any integer
as they are closely related to their decomposition into primes.

But the real trouble, as already pointed out in Fran=E7ois Le Lionnais
book "Les nombres remarquables", is that being the least non-remarkable
integer is a remarkable property...
Perhaps could we call these unreachable numbers "cretan" ones ?

Olivier

PS: I recall all seqfan members that I would like message titles to
be prefixed with [seqfan]. Thanks in advance.