A210884 -id:A210884 - cp's OEIS frontend

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

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

Hieronymus Fischer, Apr 01 2012

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).

			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).

Hieronymus Fischer, Table of n, a(n) for n = 1..331
Index entries for sequences related to calendars

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

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

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

Hieronymus Fischer, Apr 01 2012

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).

			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).

Hieronymus Fischer, Table of n, a(n) for n = 1..335
Index entries for sequences related to calendars

Cf. A210883 - A210884, A210886 - A210895, A106605, A107273, A107275.

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

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

Hieronymus Fischer, Apr 01 2012

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.

			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).

Hieronymus Fischer, Table of n, a(n) for n = 1..331

Cf. A210883 - A210892, A210894 - A210895, A106605, A107273, A107275.

a(n)=MMDDYYYY_date('Jan 1 1000' + A210883(n)).

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

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.

cp's OEIS Frontend

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

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

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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.

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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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