20th may, Historical date!

[alexandre.wajnberg at skynet.be]

Hello dear Seqfans and friends,


Nicolas Graner (member of the Oulipo litterary movement) has devised a 
reflexion about symetric and palindromic caracters of some dates,
which is urgent to transmit to us, mad of numbers.
(and thanks to Éric Angelini for giving me this precious info!).

20th february 2002 was very palindromic indeed:
	— 20022002 —

And now approaches 20th may 2005,
	— 20052005 —
a double-symetrical date.


Explanation:
1) Old electronic clocks and cheap calculator display
the ten digits in squary figures comporting seven segments (think to 
the 8: seven segments).
0, 1 and 8 have a vertical axis of symmetry; and 2 and 5 are mutually 
symmetric. From this, 25 four digit numbers may be constructed, having 
a vertical axis of symmetry:

0000 0110 0250 0520 0880
1001 1111 1251 1521 1881
2005 2115 2255 2525 2885
5002 5112 5252 5522 5882
8008 8118 8258 8528 8888
(BTW  they are a substring of A053701)

So this year 2005 is the first symmetrical year since 124 years: 1881!
And next one is 2115!   (A rarity "Venus-transit" like)

That's for the first half of "double-symmetrical date".


2) If we consider the eight digits dates DDMMYYYY, there is, according 
to Nicolas Graner, 98 such symmetrical dates.
(the / are only for the lisibility and don't participate to the 
symmetry):

10/10/0101 20/10/0105 01/10/0110 11/10/0111 21/10/0115 05/10/0120
15/10/0121 25/10/0125 02/10/0150 12/10/0151 22/10/0155 08/10/0180
18/10/0181 28/10/0185 10/01/1001 20/01/1005 01/01/1010 11/01/1011
21/01/1015 05/01/1020 15/01/1021 25/01/1025 02/01/1050 12/01/1051
22/01/1055 08/01/1080 18/01/1081 28/01/1085 10/11/1101 20/11/1105
01/11/1110 11/11/1111 21/11/1115 05/11/1120 15/11/1121 25/11/1125
02/11/1150 12/11/1151 22/11/1155 08/11/1180 18/11/1181 28/11/1185
10/05/2001 20/05/2005 01/05/2010 11/05/2011 21/05/2015 05/05/2020
15/05/2021 25/05/2025 02/05/2050 12/05/2051 22/05/2055 08/05/2080
18/05/2081 28/05/2085 10/02/5001 20/02/5005 01/02/5010 11/02/5011
21/02/5015 05/02/5020 15/02/5021 25/02/5025 02/02/5050 12/02/5051
22/02/5055 08/02/5080 18/02/5081 28/02/5085 10/12/5101 20/12/5105
01/12/5110 11/12/5111 21/12/5115 05/12/5120 15/12/5121 25/12/5125
02/12/5150 12/12/5151 22/12/5155 08/12/5180 18/12/5181 28/12/5185
10/08/8001 20/08/8005 01/08/8010 11/08/8011 21/08/8015 05/08/8020
15/08/8021 25/08/8025 02/08/8050 12/08/8051 22/08/8055 08/08/8080
18/08/8081 28/08/8085
(Removing the 28 dates beginning with 0 and re-arranging the rest in
increasing order gives another sequence we are submitting.)


The 10/05/2001 was the first symmetrical eight digits date since eight 
centuries!

And now comes the point: if we take from this list the symmetrical 
dates both for the eight digits AND for the year, there is only four 
such dates:

01/10/0110
10/01/1001
11/11/1111
20/05/2005

The first one doesn't count because of the beginning zero of the year;
and the two next ones where ok but in the countries were time was ruled 
by the christian calendar, the 0 was not in use! So the people were not 
conscious of this feature of these two days.
Conclusion :

           		 Friday the 20 may 2005
									 —  20052005 —

					will be the only day in the whole
					past, present and future story of
					our calendar where human being will
					have the opportunity to be fully
					conscious to live a date presenting
					a vertical axis of symmetry both for
				  its eight digits and for its two halves.
								
					

How will the Seqfans and friends celebrate this historical and 
planetary event?

Have a nice non-symmetrical day.

  Alexandre
(but symmetrical year!)