[seqfan] Re: A090709 Decimal primes whose decimal representation in base 6 is also prime. -- rebasing

[Maximilian Hasler]

> the listed data values for the sequence A007088
>
>   1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110...
>
> Worse, carefully read, the description of A007088 is ambiguous and/or
> formally inconsistent.  The very first comment says "Or, numbers that are
> sums of distinct powers of 10."  So is the value listed for a(2) to be
> interpreted as two or as ten?  In binary the first prime value is a(1), but
> interpreted as sums of distinct powers of 10 it is a(2).  Which is it?

IMHO, the first comment is the "correct" description of the sequence,
and the (current...) "official name" is strictly speaking incorrect,
but maybe preferable to what would be a rigorously correct way to say
what is meant. (e.g., cf. A067894 below, "Write numbers in base 2 and
read them as decimal numbers". Or in that sense - actually, I strongly
dislike the expression "decimal numbers" (and partially eliminated it
in some of the earlier mentioned edits), I think there is no such
thing, "decimal number" (or rather, it does mean something different,
namely rationals that have a finite representation in base 10, i.e.,
which are an integer when multiplied with a sufficiently high power of
10))

E.g., the first differences of this sequence are:
A138342         First differences of A007088.
9, 1, 89, 1, 9, 1, 889, 1, 9, 1, 89, 1,...

and partial sums are
A067894         Write 0, 1, ..., n in binary and add as if they were
decimal numbers.
0, 1, 11, 22, 122, 223, 333, 444, 1444, 2445, 3455, 4466

Superseeker would certainly use the same "rules".
I think, too, that OEIS is/should remain what it is in view of its
name (namely, the terms are integers and not strings) and one could
imagine, just like switching languages, to switch the way these
integers are displayed (e.g., in some base other than 10, or, e.g.,
spoken ; then A007088(2) would most certainly be read "ten" in
English, unless major modifications are implemented. I'm not against a
base:B keyword, but it should rather serve as a "rebase-link" (i.e.,
"read terms as (if they /were/) base B numbers, and show the
corresponding value - in decimal or English speech or pictograms or
whatever") than mean: the "strings" in the data line are not the
decimal representation of integers.

Maximilian