A106605 -id:A106605 - cp's OEIS frontend

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.

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

Hieronymus Fischer, Apr 01 2012

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.

			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).

Hieronymus Fischer, Table of n, a(n) for n = 1..214

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

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

Hieronymus Fischer, Apr 01 2012

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.

			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).

Hieronymus Fischer, Table of n, a(n) for n = 1..335

Cf. A210883 - A210885, A210887 - A210895, A106605, A107273, A107275.

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

Hieronymus Fischer, Apr 01 2012

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".

			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).

Hieronymus Fischer, Table of n, a(n) for n = 1..30
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

Cf. A210883-A210886, A210888-A210895, A106605, A107273, A107275.

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)

A210888 Dates after Jan 01 00 in chronological order which are palindromic when they are written in the format DD.MM.YY. The terms are listed as numbers (without the dots). Leading zeros of the terms are suppressed.

Original entry on oeis.org

101101, 201102, 301103, 11110, 111111, 211112, 21120, 121121, 221122, 31130, 131131, 231132, 41140, 141141, 241142, 51150, 151151, 251152, 61160, 161161, 261162, 71170, 171171, 271172, 81180, 181181, 281182, 91190, 191191, 291192

Offset: 1

Hieronymus Fischer, Apr 01 2012

There are exactly 30 such palindromic dates between Jan 1 00 and Dec 31 99 (see b-file for the complete list).

See A210887 for the number of days after 'Mar 1 00' to get such a palindromic date.

			The first palindromic date in DD.MM.YY format after 'Jan 01 00' is a(1)=101101 (='10.11.01' = 'Nov 10 01' = 'Mar 01 00' + A210887(1) days);
The sixth palindromic date in DD.MM.YY format after 'Jan 01 00' is a(6)=211112 (='21.11.12' = 'Nov 21 12' = 'Mar 01 00' + A210887(6) days).
The last (30th) palindromic date in DD.MM.YY format after 'Jan 01 00' is a(30)=291192 (='29.11.92' = 'Nov 29 92' = 'Mar 01 00' + A210887(30) days).

Hieronymus Fischer, Table of n, a(n) for n = 1..30
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Cf. A210883 - A210887, A210889 - A210895, A106605, A107273, A107275

a(n) = DDMMYY_date('Mar 1 00' + A210887(n)).
From Chai Wah Wu, Feb 03 2021: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n > 7.
G.f.: x*(100001*x^6 - 391094*x^3 + 100001*x^2 + 100001*x + 101101)/(x^4 - x^3 - x + 1). (End)

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

Hieronymus Fischer, Apr 01 2012

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'.

			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).

Hieronymus Fischer, Table of n, a(n) for n = 1..24

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

A213182 Numbers which may represent a date in "condensed European notation" DDMMYY.

Original entry on oeis.org

10100, 10101, 10102, 10103, 10104, 10105, 10106, 10107, 10108, 10109, 10110, 10111, 10112, 10113, 10114, 10115, 10116, 10117, 10118, 10119, 10120, 10121, 10122, 10123, 10124, 10125, 10126, 10127, 10128, 10129, 10130, 10131, 10132, 10133, 10134, 10135, 10136, 10137, 10138, 10139, 10140

Offset: 1

M. F. Hasler, Feb 27 2013

The "may" in the definition should clarify that, e.g., 290200 is in the sequence since it may represent a date, but not necessarily in any century.
The sequence is finite, the largest term is a(36525)=311299.
There are 366*25 + 365*75 = 36525 possible dates. - Giovanni Resta, Feb 28 2013

			a(1)=10100 represents e.g., Jan 01 1900 or Jan 01 2000.
a(100)=10199 (for Jan 01 1999) is followed by a(101)=10200 (for Feb 01 2000).
a(1200)=11299 (for Dec 01 1999) is followed by a(1201)=20100 (for Jan 02 2000).
The sequence becomes more interesting after the term 281299, since then the numbers DD02YY drop out for DD > 29 and for DD = 29 depending on YY.

Cf. A213184; A106605, A107273, A107275; A210883, A210884, A210885.

A213184 Numbers which may represent a date in "condensed American notation" MMDDYY.

Original entry on oeis.org

10100, 10101, 10102, 10103, 10104, 10105, 10106, 10107, 10108, 10109, 10110, 10111, 10112, 10113, 10114, 10115, 10116, 10117, 10118, 10119, 10120, 10121, 10122, 10123, 10124, 10125, 10126, 10127, 10128, 10129, 10130, 10131, 10132, 10133, 10134, 10135, 10136, 10137, 10138, 10139, 10140

Offset: 1

M. F. Hasler, Feb 28 2013

The "may" in the definition should clarify that, e.g., 22900 is in the sequence since it may represent a date (Feb. 29), but not necessarily in any century (e.g., in 2000 but not in 1900), but 22900+k is present only for k=0 (mod 4).

The sequence is finite, with 366*25 + 365*75 terms, cf. comment from G. Resta in A213182. The largest term is a(36525)=123199.

			a(1)=10100 represents, e.g., Jan 01 1900 (or Jan 01 2000).
a(100)=10199 (for Jan 01 1999) is followed by a(101)=10200 (for Jan 02 2000).
a(3100)=13199 (for Jan 31 1999) is followed by a(3101)=20100 (for Feb 01 2000).

Cf. A213182, A106605, A107273, A107275; A210883, A210884, A210885.

A107276 Vertically symmetrical dates DDMMYY ("condensed European notation") considered as numbers, in increasing order.

Original entry on oeis.org

101101, 111111, 121151, 151121, 181181, 201105, 211115, 221155, 251125, 281185

Offset: 1

Alexandre Wajnberg, May 19 2005

2 and 5 are taken as mirror images (as on calculator displays). From now on, the next symmetric date is November 20 2005 (201105). a(1)=101101, a(2)=111111 and a(5)=181181 share the property to present also two symmetrical halves. Next one is November 11 2011 (11 11 11).

Next one is Nov 21 2015 (211115). - M. F. Hasler, Feb 27 2013

Cf. A053701, A106605.

A107276(n)=101101+[8008,0,1001,2005,5002][n%5+1]*10+n\6*100004 \\ M. F. Hasler, Feb 28 2013

Edited by Jon E. Schoenfield, Feb 10 2015

A107274 Vertically symmetrical dates MMDDYY ("condensed American notation") considered as numbers, in increasing order.

Original entry on oeis.org

101101, 102501, 111111, 112511, 121151, 122551

Offset: 1

Alexandre Wajnberg, May 19 2005

2 and 5 are taken as mirror images (as on calculator displays). a(1)=101101 and a(3)=111111, share the property to present also two symmetrical halves. From now on, the next one is Nov 11th 11.

Cf. A053701, A106605.

A107285 a(n) = 5401(10^n + 1).

Original entry on oeis.org

4010, 22055, 202505, 2007005, 20052005, 200502005, 2005002005, 20050002005, 200500002005, 2005000002005, 20050000002005, 200500000002005, 2005000000002005, 20050000000002005, 200500000000002005, 2005000000000002005, 20050000000000002005, 200500000000000002005

Offset: 0

Reinhard Zumkeller, May 20 2005

			a(4) = 5*401*10001 = 20052005 = A106605(38).

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A062397, A106605.

2005(10^Range[0,20]+1) (* or *) LinearRecurrence[{11,-10},{4010,22055},20] (* Harvey P. Dale, Sep 06 2016 *)

my(x='x+O('x^18)); Vec(2005*(2-11*x)/((10*x-1)*(x-1))) \\ Elmo R. Oliveira, Jun 16 2025

a(n) = 2005*A062397(n).
From Elmo R. Oliveira, Jun 16 2025: (Start)
G.f.: 2005*(2-11*x)/((1-x)*(1-10*x)).
E.g.f.: 2005*exp(x)*(1 + exp(9*x)).
a(n) = 10*a(n-1) - 18045.
a(n) = 11*a(n-1) - 10*a(n-2). (End)

More terms from Elmo R. Oliveira, Jun 16 2025

cp's OEIS Frontend

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.

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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.

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

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A210888 Dates after Jan 01 00 in chronological order which are palindromic when they are written in the format DD.MM.YY. The terms are listed as numbers (without the dots). Leading zeros of the terms are suppressed.

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

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A213182 Numbers which may represent a date in "condensed European notation" DDMMYY.

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A213184 Numbers which may represent a date in "condensed American notation" MMDDYY.

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A107276 Vertically symmetrical dates DDMMYY ("condensed European notation") considered as numbers, in increasing order.

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A107274 Vertically symmetrical dates MMDDYY ("condensed American notation") considered as numbers, in increasing order.

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A107285 a(n) = 5*401*(10^n + 1).

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A107285 a(n) = 5401(10^n + 1).