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 1-10 of 14 results. Next

A210895 Dates after Jan 01 00 in chronological order which are palindromic when they are written according to the format MMDDYY (American standard, short). Leading zeros of the terms are suppressed.

Original entry on oeis.org

101101, 102201, 11110, 12210, 111111, 112211, 21120, 22220, 121121, 122221, 31130, 32230, 41140, 42240, 51150, 52250, 61160, 62260, 71170, 72270, 81180, 82280, 91190, 92290
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 A210894 for the number of days after 'Mar 1 00' to get such a palindromic date.

Examples

			The first palindromic date in MMDDYY format after 'Jan 01 00' is a(1)=101101 (= 'Oct 11 01' = 'Mar 01 00' + A210894(1) days);
The third palindromic date in MMDDYY format after 'Jan 01 00' is a(3)=11110=011110 (= 'Jan 11 10' = 'Mar 01 00' + A210894(3) days);
The 10th palindromic date in MMDDYY format after 'Jan 01 00' is a(10)=122221 (= 'Dec 22 21' = 'Mar 01 00' + A210894(10) days).
The last (24th) palindromic date in MMDDYY format after 'Jan 01 00' is a(24)=92290=092290 (= 'Sep 22 90' = 'Mar 01 00' + A210894(24) days).
		

Crossrefs

Formula

a(n) = MMDDYY_date('Mar 1 00' + A210894(n)).

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).
		

Crossrefs

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).

A210885 Number of days after Jan 01 1000 such that the date written in the format DDMMYYYY is palindromic.

Original entry on oeis.org

374, 749, 1124, 3652, 4027, 4402, 4778, 7305, 7681, 8056, 10959, 11334, 11709, 14612, 14988, 15363, 18266, 18641, 19016, 21919, 22295, 22670, 25573, 25948, 26323, 29226, 29602, 29977, 32880, 33255, 33630, 37202, 37577, 37952, 40480, 40855, 41231, 44134, 44509
Offset: 1

Views

Author

Hieronymus Fischer, Apr 01 2012

Keywords

Comments

There are exactly 335 palindromic dates between Jan 1 1000 and Dec 31 9999 (see b-file for the complete list).
See A210886 for the corresponding dates.
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 terms representing a date after 1582 (these are the terms with n higher than 61). The value 5 comes from the 10 skipped "Gregorian" days 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 10022001 which is the 62nd term of the sequence A210886. The resulting number of days after Jan 01 2000 are 406, 781, 3684, 4059, 4434, 7337, 7713, 8088, 10991, 11366, 11741, 14644, 15020, 15395, 18298, ... for the 62nd, 63rd, ... 76th ... palindromic dates (see A210886).

Examples

			The first palindromic date in DDMMYYYY format after 'Jan 01 1000' is A210886(1)=10011001 (= 'Jan 10 1001' = 'Jan 01 1000' + 374 days);
The fourth palindromic date in DDMMYYYY format after 'Jan 01 1000' is A210886(4)=1011010=01011010 (= 'Jan 01 1010' = 'Jan 01 1000' + 3652 days);
The 66th palindromic date in DDMMYYYY format after 'Jan 01 1000' is A210886(66)=21022012 (= 'Feb 21 2012' = 'Jan 01 1000' + 369676 days = 'Jan 1 2000' + 4434 days)
The last (335th) palindromic date in DDMMYYYY format before the year 10000 is A210886(335)=29099092 (= 'Sep 29 9092' = 'Jan 01 1000' + 2955814 days).
		

Crossrefs

Formula

n-th number of days after 'Jan 01 2000' = a(61+n)-365242.

A210889 Number of days after Mar 01 00 such that the date written in the format D.M.YY (and considered as a number without the dots) is palindromic.

Original entry on oeis.org

315, 346, 374, 405, 435, 466, 496, 527, 558, 619, 690, 721, 749, 780, 810, 841, 871, 902, 933, 994, 1065, 1124, 1155, 1185, 1216, 1246, 1277, 1308, 1369, 3958, 3968, 3999, 4027, 4058, 4088, 4119, 4149, 4180, 4211, 4231, 4262, 4272, 4292, 4324, 4343, 4374, 4403, 4434, 4464, 4495, 4525, 4556, 4587, 4598, 4629, 4648, 4659, 4691, 4719, 4778, 4839, 4900
Offset: 1

Views

Author

Hieronymus Fischer, Apr 01 2012

Keywords

Comments

There are exactly 322 such palindromic dates between Mar 1 00 and Dec 31 99 (see b-file for the complete list).
See A210890 for the corresponding dates.
The definition is different from A210891 in that the dates are considered as numbers.
The reference date Mar 1 00 makes sense, since this definition results 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 D.M.YY format after 'Jan 01 00' is A210890(1)=10101 (= '10.1.01' = 'Jan 10 01' = 'Mar 01 00' + 315 days);
The 10th palindromic date in D.M.YY format after 'Jan 01 00' is A210890(10)=101101 (= '10.11.01' = 'Nov 10 01' = 'Mar 01 00' + 619 days);
The 44th palindromic date in D.M.YY format after 'Jan 01 00' is A210890(44)=2112 (= '2.1.12' = 'Jan 2 12' = 'Mar 01 00' + 4324 days);
The last (322nd) palindromic date in D.M.YY format after 'Jan 01 00' is A210890(322)=9999 (= '9.9.99' = 'Sep 09 99' = 'Mar 01 00' + 36351 days).
		

Crossrefs

A210893 Dates after Jan 01 1000 in chronological order which are palindromic when they are written according to the format MMDDYYYY (American standard). Leading zeros of the terms are suppressed.

Original entry on oeis.org

10011001, 1011010, 11011011, 2011020, 12011021, 3011030, 4011040, 5011050, 6011060, 7011070, 8011080, 9011090, 10111101, 1111110, 11111111, 2111120, 12111121, 3111130, 4111140, 5111150, 6111160, 7111170, 8111180, 9111190, 10211201, 1211210, 11211211, 2211220, 12211221
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 MMDDYYYY format are also palindromic in the YYYYMMDD format. Consequently, this sequence represents the same dates as A210884.
See A210883 for the number of days after Jan 1 1000 to get such a palindromic date.
The first such palindromic dates after Jan 01 2000 are 10022001, 1022010, 11022011, 2022020, 12022021, 3022030, 4022040, 5022050, 6022060, 7022070, 8022080, 9022090, 10122101, which are the 44th, 45th, ... 56th ... dates of the original sequence.

Examples

			The first palindromic date in MMDDYYYY format after 'Jan 01 1000' is a(1)=10011001 (= 'Oct 01 1001' = 'Jan 01 1000' + A210893(1) days);
The second palindromic date in MMDDYYYY format after 'Jan 01 1000' is a(2)=1011010=01011010 (= 'Jan 01 1010' = 'Jan 01 1000' + A210893(2) days);
The 47th palindromic date in MMDDYYYY format after 'Jan 01 1000' is a(47)=2022020=02022020 (= 'Feb 02 2020' = 'Jan 01 1000' + A210893(47) days).
The last (331st) palindromic date in MMDDYYYY format before the year 10000 is a(331)=9299290=09299290 (= 'Sep 29 9290' = 'Jan 01 1000' + A210893(331) days).
		

Crossrefs

Formula

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

A210890 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 (without the dots).

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, 1111, 11111, 11211, 11311, 11411, 11511, 11611, 11711
Offset: 1

Views

Author

Hieronymus Fischer, Apr 01 2012

Keywords

Comments

There are exactly 322 such palindromic dates between Mar 1 00 and Dec 31 99 (see b-file for the complete list).
See A210889 for the number of days after 'Mar 1 00' to get such a palindromic date.
The definition is different from A210892 in that the dates are considered as numbers.
Some numbers occur twice since the dates are not unique without the dots. For example, the number 11211 may represent the date 11.2.11 (Feb 11 11) or 1.12.11 (Dec 1 11). The complete list of such dates is 11.1.11, 11.2.11, 1.11.11, 1.12.11, 21.1.12, 21.2.12, 2.11.12, 2.12.12, 31.1.13 and 3.11.13 which correspond to the terms with n=31,32,41,43,45,46,55,57,59 and 65.

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' + A210889(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' + A210889(10) days);
The 44th palindromic date in D.M.YY format after 'Jan 01 00' is a(44)=2112 (= '2.1.12' = 'Jan 2 12' = 'Mar 01 00' + A210889(44) days);
The last (322nd) palindromic date in D.M.YY format after 'Jan 01 00' is a(322)=9999 (= '9.9.99' = 'Sep 09 99' = 'Mar 01 00' + A210889(322) days).
		

Crossrefs

Formula

a(n) = DMYY_date('Mar 1 00' + A210889(n)).

A210891 Number of days after Mar 01 00 such that the date written in the format D.M.YY is palindromic.

Original entry on oeis.org

315, 346, 374, 405, 435, 466, 496, 527, 558, 619, 690, 721, 749, 780, 810, 841, 871, 902, 933, 994, 1065, 1124, 1155, 1185, 1216, 1246, 1277, 1308, 1369, 3968, 3999, 4027, 4058, 4088, 4119, 4149, 4180, 4211, 4272, 4343, 4374, 4403, 4434, 4464
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).
The definition is different from A210889/A210890 in that the palindrome property is evaluated including the dots.
See A210892 for the corresponding dates.
The reference date Mar 1 00 makes sense, since this definition results 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 D.M.YY format after 'Jan 01 00' is A210892(1)=10101 (='10.1.01'= 'Jan 10 01' = 'Mar 01 00' + 315 days);
The 10th palindromic date in D.M.YY format after 'Jan  01 00' is A210892(10)=101101 (='10.11.01'= 'Nov 10 01' = 'Mar 01 00' + 619 days);
The 44th palindromic date in D.M.YY format after 'Mar 01 00' is A210892(44)=21512 (='21.5.12'= 'May 21 12' = 'Mar 01 00' + 4464 days);
The last (214th) palindromic date in D.M.YY format after 'Mar 01 00' is A210892(214)=291192 (='29.11.92'= 'Nov 29 92' = 'Mar 01 00' + 33876 days).
		

Crossrefs

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).
		

Crossrefs

Formula

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

A210886 Dates after Jan 01 1000 in chronological order which are palindromic when they are written in the format DDMMYYYY. Leading zeros of the terms are suppressed.

Original entry on oeis.org

10011001, 20011002, 30011003, 1011010, 11011011, 21011012, 31011013, 2011020, 12011021, 22011022, 3011030, 13011031, 23011032, 4011040, 14011041, 24011042, 5011050, 15011051, 25011052, 6011060, 16011061, 26011062, 7011070, 17011071, 27011072, 8011080, 18011081, 28011082, 9011090, 19011091
Offset: 1

Views

Author

Hieronymus Fischer, Apr 01 2012

Keywords

Comments

There are exactly 335 such palindromic dates between Jan 1 1000 and Dec 31 9999 (see b-file for the complete list).
See A210885 for the number of days after 'Jan 1 1000' to get such a palindromic date.
The first palindromic dates after 'Jan 01 2000' are 10022001, 20022002, 1022010, 11022011, 21022012, 2022020, 12022021, 22022022, 3022030, 13022031, 23022032, 4022040, 14022041, 24022042, 5022050, ... which are the 62nd, 63rd, ... 76th ... dates of the original sequence.

Examples

			The first palindromic date in DDMMYYYY format after 'Jan 01 1000' is a(1)=10011001 (= 'Jan 10 1001' = 'Jan 01 1000' + A210885(1) days);
The fourth palindromic date in DDMMYYYY format after 'Jan 01 1000' is a(4)=1011010=01011010 (= 'Jan 01 1010' = 'Jan 01 1000' + A210885(4) days);
The 66th palindromic date in DDMMYYYY format after 'Jan 01 1000' is a(66)=21022012 (= 'Feb 21 2012' = 'Jan 01 1000' + A210885(66) days)
The last (335th) palindromic date in DDMMYYYY format before the year 10000 is a(335)=29099092 (= 'Sep 29 9092' = 'Jan 01 1000' + A210885(335) days).
		

Crossrefs

Formula

a(n)=DDMMYYYY_date('Jan 1 1000' + A210885(n)).
n-th date after 'Jan 1 2000' = a(61+n).

A210887 Number of days after Mar 01 00 such that the date written in the format DD.MM.YY is palindromic.

Original entry on oeis.org

619, 994, 1369, 3897, 4272, 4648, 7551, 7926, 8301, 11204, 11579, 11955, 14858, 15233, 15608, 18511, 18886, 19262, 22165, 22540, 22915, 25818, 26193, 26569, 29472, 29847, 30222, 33125, 33500, 33876
Offset: 1

Views

Author

Hieronymus Fischer, Apr 01 2012

Keywords

Comments

There are exactly 30 such palindromic dates between Jan 01 00 and Dec 31 99 (see b-file for the complete list).
See A210888 for the corresponding dates.
The reference date Mar 01 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 DD.MM.YY format after "Jan 01 00" is A210888(1)=101101 (="10.11.01"= "Nov 10 01" = "Mar 01 00" + 619 days);
The sixth palindromic date in DD.MM.YY format after "Jan 01 00" is A210888(6)=211112 (="21.11.12"= "Nov 21 12" = "Mar 01 00" + 4648 days).
The last (30th) palindromic date in DD.MM.YY format after "Jan 01 00" is A210888(30)=291192 (="29.11.92"= "Nov 29 92" = "Mar 01 00" + 33876 days).
		

Crossrefs

Formula

From Chai Wah Wu, Feb 03 2021: (Start)
a(n) = a(n-1) + a(n-6) - a(n-7) for n > 10.
G.f.: x*(375*x^9 + 2284*x^6 + 376*x^5 + 375*x^4 + 2528*x^3 + 375*x^2 + 375*x + 619)/(x^7 - x^6 - x + 1). (End)
Showing 1-10 of 14 results. Next