cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A210883 Number of days after Jan 01 1000 such that the date written in the ISO-8601-format YYYYMMDD is palindromic.

Original entry on oeis.org

638, 3652, 4321, 7335, 8004, 11016, 14700, 18382, 22066, 25748, 29432, 33115, 37172, 40186, 40855, 43869, 44538, 47550, 51234, 54916, 58600, 62282, 65966, 69649, 73707, 76721, 77390, 80404, 81073, 84085, 87769, 91451, 95135, 98817, 102501, 106184, 110241
Offset: 1

Views

Author

Hieronymus Fischer, Apr 01 2012

Keywords

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).

Examples

			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).

Links

Crossrefs

Cf. A210884 - A210895, A106605, A107273, A107275.

Formula

n-th number of days after 'Jan 01 2000' = a(43+n) - 365242.

A210884 Dates after Jan 01 1000 which are palindromic when they are written according to the ISO-8601-format YYYYMMDD.

Original entry on oeis.org

10011001, 10100101, 10111101, 10200201, 10211201, 10300301, 10400401, 10500501, 10600601, 10700701, 10800801, 10900901, 11011011, 11100111, 11111111, 11200211, 11211211, 11300311, 11400411, 11500511, 11600611, 11700711, 11800811, 11900911, 12011021, 12100121, 12111121, 12200221, 12211221, 12300321, 12400421, 12500521, 12600621, 12700721, 12800821, 12900921
Offset: 1

Views

Author

Hieronymus Fischer, Apr 01 2012

Keywords

Comments

There are exactly 331 such palindromic dates between Jan 1 1000 and Dec 31 9999 (see b-file for the complete list).
Dates palindromic in the YYYYMMDD format are also palindromic in the MMDDYYYY format. Consequently, this sequence represents the same dates as A210893.
See A210883 for the number of days after Jan 1 1000 to get such a palindromic date.
The first palindromic dates after 'Jan 01 2000' are 20011002, 20100102, 20111102, 20200202, 20211202, 20300302, 20400402, 20500502, 20600602, 20700702, 20800802, 20900902, 21011012 which are the 44th, 45th, ... 56th ... dates of the original sequence.

Examples

			The first palindromic date in YYYYMMDD format after 'Jan 01 1000' is a(1)=10011001 (= 'Oct 01 1001' = 'Jan 01 1000' + A210883(1) days);
The 47th palindromic date in YYYYMMDD format after 'Jan 01 1000' is a(47)=20200202 (= 'Feb 02 2020' = 'Jan 01 1000' + A210883(47) days).
The last (331st) palindromic date in YYYYMMDD format before the year 10000 is a(331)=92900929 (= 'Sep 29 9290' = 'Jan 01 1000' + A210883(331) days).

Links

Crossrefs

Cf. A210883, A210885 - A210895, A106605, A107273, A107275.

Programs

  • Mathematica
    Select[StringDelete[#,"-"]&/@(DateString[#,"ISODate"]&/@DateRange[{1000,1,1},{9999,12,31}]),PalindromeQ]//ToExpression  (* Harvey P. Dale, Dec 24 2023 *)

Formula

a(n)=YYYYMMDD_date('Jan 1 1000' + A210883(n)).
n-th date after 'Jan 1 2000' = a(43+n).

A210892 Dates after Jan 01 00 in chronological order which are palindromic when they are written in the format D.M.YY. The terms are listed as numbers. Leading zeros of the terms are suppressed.

Original entry on oeis.org

10101, 10201, 10301, 10401, 10501, 10601, 10701, 10801, 10901, 101101, 20102, 20202, 20302, 20402, 20502, 20602, 20702, 20802, 20902, 201102, 30103, 30303, 30403, 30503, 30603, 30703, 30803, 30903, 301103, 11111, 11211, 11311, 11411, 11511, 11611, 11711
Offset: 1

Views

Author

Hieronymus Fischer, Apr 01 2012

Keywords

Comments

There are exactly 214 such palindromic dates between Jan 1 00 and Dec 31 99 (see b-file for the complete list).
See A210891 for the number of days after 'Mar 1 00' to get such a palindromic date.
The definition is different from A210889/A210890 in that the palindrome property is evaluated including the dots.
To get a real date from a term, insert a dot between the second and the third digit from the left and between the second and the third digit from the right.

Examples

			The first palindromic date in D.M.YY format after 'Jan 01 00' is a(1)=10101 (='10.1.01'= 'Jan, 10 01' = 'Mar 01 00' + A210891(1) days);
The 10th palindromic date in D.M.YY format after 'Jan  01 00' is a(10)=101101 (='10.11.01'= 'Nov 10 01' = 'Mar 01 00' + A210891(10) days);
The 44th palindromic date in D.M.YY format after 'Jan  01 00' is a(44)=21512 (='21.5.12'= 'May 21 12' = 'Mar 01 00' + A210891(44) days);
The last (214th) palindromic date in D.M.YY format after 'Jan 01 00' is a(214)=291192 (='29.11.92'= 'Nov 29 92' = 'Mar 01 00' + A210891(214) days).

Links

Crossrefs

Cf. A210883 - A210891, A210893 - A210895, A106605, A107273, A107275

Formula

a(n)=DMYY_date('Mar 1 00' + A210891(n)).

A210894 Number of days after Mar 01 00 such that the date written the format MMDDYY (American standard, short) is palindromic.

Original entry on oeis.org

589, 600, 3603, 3614, 4272, 4283, 7255, 7297, 7955, 7966, 10967, 10978, 14651, 14662, 18333, 18344, 22017, 22028, 25699, 25710, 29383, 29394, 33066, 33077
Offset: 1

Views

Author

Hieronymus Fischer, Apr 01 2012

Keywords

Comments

There are exactly 24 such palindromic dates between Jan 1 00 and Dec 31 99 (see b-file for the complete list).
See A210895 for the corresponding dates.
The reference date Mar 1 00 makes sense, since this result in a sequence which is independent from the leap year / non-leap year property of the reference year '00'.

Examples

			The first palindromic date in MMDDYY format after 'Jan 01 00' is A210895(1)=101101 (= 'Oct 11 01' = 'Mar 01 00' + 589 days);
The third palindromic date in MMDDYY format after 'Jan 01 00' is A210895(3)=11110=011110 (= 'Jan 11 01' = 'Mar 01 00' + 3603 days);
The 10th palindromic date in MMDDYY format after 'Jan 01 00' is A210895(10)=122221 (= 'Dec 22 21' = 'Mar 01 00' + 7966 days).
The last (24th) palindromic date in MMDDYY format after 'Jan 01 00' is A210895(24)=92290=092290 (= 'Sep 22 90' = 'Mar 01 00' + 33077 days).

Links

Crossrefs

Cf. A210883 - A210893, A210895, A106605, A107273, A107275.
Showing 1-4 of 4 results.

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