[seqfan] Re: Primes where every other digit is 1

M. F. Hasler seqfan at hasler.fr
Fri Oct 22 23:57:33 CEST 2021

```Numbers having this property in base 2 are listed in A002450, the only such
prime is 5 = 101_2.

Yes, as Frank mentioned, you must say "only" (exclude e.g. 11) and that you
start with a 1 from the right / the last digit (not e.g. 13, 17, 19, 1x1y
etc, I suppose).
Would you read from left to right, "every other" makes indeed more sense
for x1y1z1..., but then 101, 131... should not be there, strictly speaking.
So I infer you read from right to left and "every other" means actually
that the second, fourth etc digit (from the right) must *not* be 1.

So that is quite a special pattern: so special that even the sequence of
*numbers* (disregarding primality) of that form is not in the OEIS:
Dozens of hits for 21,31,...,91,
9 hits when you append 101,
None if you also append 121.
(Also no hit for the more logical variant, if I dare to say so, where the
91 is followed by 2101.
Also not in the OEIS, the variant where "every other" means odd positions
(1st, 3rd... digit), starting from the left, not right.)

In such a case, I think we should have/add the list of all such *numbers*
(here: 1, 21, 31, ..., 91, 101, 121,...), before considering *primes*
within that list.

That list could also Xref Eric Angelini's A276103 where also only every
other digit is 1.

-Maximilian

On Thu, Oct 21, 2021, 20:59 Lars Blomberg <lars.blomberg2 at hotmail.com>
wrote:

> Hello,
>
> Is this of interest:
> 31,41,61,71,101,131,151,181,191,2131,2141, ...
> ?
> ... or 3,7,9.
>
> /Lars Blomberg
>

```