# [seqfan] Re: Commas squeezed between two same parity digits

M. F. Hasler oeis at hasler.fr
Thu Oct 30 19:56:18 CET 2014

```On Fri, Oct 24, 2014 at 7:44 AM, M. F. Hasler <oeis at hasler.fr> wrote:
> On Fri, Oct 24, 2014 at 7:04 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>> Hello SeqFans,
>> a(n+1) is the smallest unused yet integer such that
>> the first digit of a(n+1) has the parity of the last digit of a(n).
>>
>> P = 0,2,4,6,8,20,21,1,3,5,7,9,10,22,23,11,12,24,25,13,14,26,27,15,16,28,29,17,18,40,41,19,30,...
>
> Next term is 42 ! ;-)
> Proposed as https://oeis.org/draft/A249278

I just proposed the corresponding permutation of positive integers,
1, 3, 5, 7, 9, 10, 2, 4, 6, 8, 20, 21, 11, 12, 22, 23, 13, 14, 24, 25,
15, 16, 26, 27, 17, 18, 28, 29, 19, 30, 40, 41, 31, 32, 42, 43, 33,
34, 44, 45, 35, 36, 46, 47, 37, 38, 48, 49, 39, 50, 60, 61, 51, 52,
62, 63, 53, 54, 64, 65, 55, 56, 66, 67, 57, 58, 68, 69, 59, 70, 80,
81, 71, 72, 82, 83, 73, 74, 84, 85, 75, 76, 86, 87, 77, 78, 88, 89,
79, 90, 200
as https://oeis.org/draft/A249494

Actually I "discovered" this yesterday night by suggesting this game
as "good night story" to my little daughter :-)
I was astonished not to find the result on OEIS...

Then we played the similar game with equality instead of parity and rediscovered
A162501 = smallest permutation of the natural numbers such that the
initial digit for each term is equal to the last non-zero digit of its
predecessor.

Maximilian

```