OFFSET
1,1
COMMENTS
There are exactly 331 palindromic dates between Jan 1 1000 and Dec 31 9999 (see b-file for the complete list).
See A210884 for the corresponding dates.
These are also the numbers of days after Jan 01 1000 such that the date written in the format MMDDYYYY is palindromic (see A210893).
Because of the Gregorian Calendar Reform of 1582 these terms are fictitious, strictly speaking. They are valid only then, if we adopt the reform for dates before 1582, subsequently. To get the real number of days after 'Jan 1 1000' for years after 1582 subtract 5 from each term representing a date after 1582 (these are the terms with n higher than 43). The value 5 comes from the 10 skipped "Gregorian" dates between Oct 4 and Oct 15 1582 minus the 5 additional Julian leap days in the years 1000, 1100, 1300, 1400 and 1500 which are not Gregorian leap years.
To determine the real number of days after 'Jan 01 2000' just subtract 365242 from each term. The first palindromic date after 'Jan 01 2000' is 20011002 which is the 44th term of the sequence A210884. The resulting number of days after 'Jan 01 2000' are 640, 3654, 4323, 7337, 8006, 11018, 14702, 18384, 22068, 25750, 29434, 33117, 37174, ... for the 44th, 45th, ... 56th ... palindromic dates (see A210884).
LINKS
Hieronymus Fischer, Table of n, a(n) for n = 1..331
FORMULA
n-th number of days after 'Jan 01 2000' = a(43+n) - 365242.
EXAMPLE
The first palindromic date in YYYYMMDD format after 'Jan 01 1000' is A210884(1)=10011001 (= 'Oct 01 1001' = 'Jan 01 1000' + 638 days);
The 47th palindromic date in YYYYMMDD format after 'Jan 01 1000' is A210884(47)=20200202 (= 'Feb 02 2020' = 'Jan 01 1000' + 372579 days = 'Jan 01 2000' + 7337 days).
The last (331st) palindromic date in YYYYMMDD format before the year 10000 is A210884(331)=92900929 (= 'Sep 29 9290' = 'Jan 01 1000' + 3028132 days).
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Hieronymus Fischer, Apr 01 2012
STATUS
approved