A119406 -id:A119406 - cp's OEIS frontend

A141287 Years in which there are five Fridays in the month of February.

1760, 1788, 1828, 1856, 1884, 1924, 1952, 1980, 2008, 2036, 2064, 2092, 2104, 2132, 2160, 2188, 2228, 2256, 2284, 2324, 2352, 2380, 2408, 2436, 2464, 2492, 2504, 2532, 2560, 2588, 2628, 2656, 2684, 2724, 2752, 2780, 2808, 2836, 2864, 2892, 2904, 2932

Offset: 1

J. Lowell, Aug 01 2008

Index entries for sequences related to calendars
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Cf. A119406 (Sun), A135795 (Mon), A143994 (Tue), A141039 (Wed), A143995 (Thu), A176478 (Sat).

A141287 := proc(n) nper := (n-1) mod 14 ; floor((n-1)/14)*400+op(1+nper ,[1760, 1788, 1828, 1856, 1884, 1924, 1952, 1980, 2008, 2036, 2064, 2092, 2104, 2132]) ; end proc: seq(A141287(n),n=1..80) ; # R. J. Mathar, Jan 25 2010

(* First do *) Needs["Calendar`"] (* then *) fQ[y_] := Mod[y, 4] == 0 && Mod[y, 400]!=0 && DayOfWeek[{y, 2, 1}] == Friday; Select[Range[1750, 3051], fQ@# &] (* Robert G. Wilson v, Jun 11 2010 *)
(* Second program, needing Mma version >= 9.0 *)
okQ[y_] := Mod[y, 4] == 0 && DayCount[{y, 1, 31}, DatePlus[{y, 3, 1}, -1], Friday] == 5;
Select[Range[1752, 3051, 4], okQ] (* Jean-François Alcover, Mar 27 2020 *)

More terms using the 400-year periodicity of the Gregorian calendar by R. J. Mathar, Jan 25 2010

A135795 Years in which there are five Mondays in the month of February.

Original entry on oeis.org

1768, 1796, 1808, 1836, 1864, 1892, 1904, 1932, 1960, 1988, 2016, 2044, 2072, 2112, 2140, 2168, 2196, 2208, 2236, 2264, 2292, 2304, 2332, 2360, 2388, 2416, 2444, 2472, 2512, 2540, 2568, 2596, 2608, 2636, 2664, 2692, 2704, 2732, 2760, 2788, 2816, 2844, 2872, 2912, 2940, 2968, 2996, 3008, 3036

Offset: 1

J. Lowell, Mar 03 2008

nonn

Index entries for sequences related to calendars
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Cf. A119406 (Sun), A143994 (Tue), A141039 (Wed), A143995 (Thu), A141287 (Fri), A176478 (Sat).

(* First do *) Needs["Calendar`"] (* then *) fQ[y_] := Mod[y, 4] == 0 && Mod[y, 400]!=0 && DayOfWeek[{y, 2, 1}] == Monday; Select[Range[1750, 3051], fQ@# &] (* Robert G. Wilson v, Jun 11 2010 *)
Select[Range[1768,3036,4],LeapYearQ[{#}]&& DayName[{#,2,1}]==Monday&] (* Harvey P. Dale, Aug 01 2017 *)

More terms from R. J. Mathar, Mar 29 2010

Corrected by Harvey P. Dale, Aug 01 2017

A141039 Years in which there are five Wednesdays in the month of February.

Original entry on oeis.org

1764, 1792, 1804, 1832, 1860, 1888, 1928, 1956, 1984, 2012, 2040, 2068, 2096, 2108, 2136, 2164, 2192, 2204, 2232, 2260, 2288, 2328, 2356, 2384, 2412, 2440, 2468, 2496, 2508, 2536, 2564, 2592, 2604, 2632, 2660, 2688, 2728, 2756, 2784, 2812, 2840, 2868, 2896, 2908, 2936, 2964, 2992, 3004, 3032

Offset: 1

J. Lowell, Jul 30 2008

nonn

Index entries for sequences related to calendars
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Cf. A119406 (Sun), A135795 (Mon), A143994 (Tue), A143995 (Thu), A141287 (Fri), A176478 (Sat).

A141039 := proc(n) nper := (n-1) mod 13 ; floor((n-1)/13)*400+op(1+nper , [1764,1792,1832,1860,1888,1928,1956,1984,2012,2040,2068,2096,2136] ) ; end proc: seq(A141039(n), n=1..80) ; # R. J. Mathar, Mar 29 2010

(* Needs Mma version >= 9.0 *)
okQ[y_] := LeapYearQ[{y}] && DayName[{y, 2, 1}] == Wednesday;
Select[Range[1752, 3051, 4], okQ] (* Jean-François Alcover, Mar 27 2020 *)

More terms from R. J. Mathar, Mar 29 2010

Missing terms inserted by Jean-François Alcover, Mar 27 2020

A143994 Years in which there are five Tuesdays in the month of February.

Original entry on oeis.org

1752, 1780, 1820, 1848, 1876, 1916, 1944, 1972, 2000, 2028, 2056, 2084, 2124, 2152, 2180, 2220, 2248, 2276, 2316, 2344, 2372, 2400, 2428, 2456, 2484, 2524, 2552, 2580, 2620, 2648, 2676, 2716, 2744, 2772, 2800, 2828, 2856, 2884, 2924, 2952, 2980, 3020, 3048

Offset: 1

J. Lowell, Sep 07 2008

nonn

Index entries for sequences related to calendars
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Cf. A119406 (Sun), A135795 (Mon), A141039 (Wed), A143995 (Thu), A141287 (Fri), A176478 (Sat).

A143994 := proc(n) nper := (n-1) mod 13 ; floor((n-1)/13)*400+op(1+nper , [1780, 1820, 1848, 1876, 1916, 1944, 1972, 2000, 2028, 2056, 2084, 2124, 2152] ) ; end proc: seq(A143994(n), n=1..80) ; # R. J. Mathar, Mar 29 2010

(* Needs Mma version >= 9.0 *)
okQ[y_] := LeapYearQ[{y}] && DayName[{y, 2, 1}] == Tuesday;
Select[Range[1752, 3051, 4], okQ] (* Jean-François Alcover, Mar 27 2020 *)

More terms from R. J. Mathar, Mar 29 2010

a(1) = 1752 inserted by Jean-François Alcover, Mar 27 2020

A143995 Years in which there are five Thursdays in the month of February, in the Gregorian calendar.

Original entry on oeis.org

1776, 1816, 1844, 1872, 1912, 1940, 1968, 1996, 2024, 2052, 2080, 2120, 2148, 2176, 2216, 2244, 2272, 2312, 2340, 2368, 2396, 2424, 2452, 2480, 2520, 2548, 2576, 2616, 2644, 2672, 2712, 2740, 2768, 2796, 2824, 2852, 2880, 2920, 2948, 2976, 3016, 3044

Offset: 1

J. Lowell, Sep 07 2008

nonn

Index entries for sequences related to calendars
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Cf. A119406 (Sun), A135795 (Mon), A143994 (Tue), A141039 (Wed), A141287 (Fri), A176478 (Sat).

A143995 := proc(n) nper := (n-1) mod 13 ; floor((n-1)/13)*400+op(1+nper , [1776, 1816, 1844, 1872, 1912, 1940, 1968, 1996, 2024, 2052, 2080, 2120, 2148] ) ; end proc: seq(A143995(n), n=1..80) ; # R. J. Mathar, Mar 29 2010

(* Needs Mma version >= 9.0 *)
okQ[y_] := LeapYearQ[{y}] && DayName[{y, 2, 1}] == Thursday;
Select[Range[1752, 3051, 4], okQ] (* Jean-François Alcover, Mar 27 2020 *)

More terms from R. J. Mathar, Mar 29 2010

A176478 Years in which there are five Saturdays in the month of February.

Original entry on oeis.org

1772, 1812, 1840, 1868, 1896, 1908, 1936, 1964, 1992, 2020, 2048, 2076, 2116, 2144, 2172, 2212, 2240, 2268, 2296, 2308, 2336, 2364, 2392, 2420, 2448, 2476, 2516, 2544, 2572, 2612, 2640, 2668, 2696, 2708, 2736, 2764, 2792, 2820, 2848, 2876, 2916, 2944, 2972, 3012, 3040

Offset: 1

Robert G. Wilson v, Apr 18 2010

nonn

Index entries for sequences related to calendars
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

Cf. A119406 (Sun), A135795 (Mon), A143994 (Tue), A141039 (Wed), A143995 (Thu), A141287 (Fri).

(* Needs Mma version >= 9.0 *)
okQ[y_] := LeapYearQ[{y}] && DayName[{y, 2, 1}] == Saturday;
Select[Range[1752, 3052, 4], okQ] (* Jean-François Alcover, Mar 27 2020 *)

Wrong years removed by J. Lowell, Apr 22 2010

Corrected and extended by Jean-François Alcover, Mar 27 2020

A174431 Day of the week occurring 5 times in February, or 0 if no such day exists (1 to 7 are Sunday to Saturday).

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 7, 0, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 7, 0, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 7

Offset: 1753

J. Lowell, Mar 19 2010

nonn

			a(1756) = 1 because February 1756 has 5 Sundays.

Index entries for sequences related to calendars

Cf. A119406 (Sundays), A135795 (Mondays), A141039 (Wednesdays).

Cf. A143994 (Tuesdays), A143995 (Thursdays).

More terms from R. J. Mathar, Apr 15 2010

a(1827)-a(1840) from Jinyuan Wang, Jun 19 2021

A242539 Years with 53 sundays in the Gregorian calendar.

Original entry on oeis.org

1584, 1589, 1595, 1600, 1606, 1612, 1617, 1623, 1628, 1634, 1640, 1645, 1651, 1656, 1662, 1668, 1673, 1679, 1684, 1690, 1696, 1702, 1708, 1713, 1719, 1724, 1730, 1736, 1741, 1747, 1752, 1758, 1764, 1769, 1775, 1780, 1786, 1792, 1797, 1804, 1809, 1815, 1820, 1826, 1832, 1837, 1843, 1848, 1854, 1860, 1865, 1871, 1876, 1882, 1888, 1893, 1899, 1905, 1911, 1916, 1922, 1928, 1933, 1939, 1944, 1950, 1956, 1961, 1967, 1972, 1978, 1984, 1989, 1995, 2000, 2006, 2012, 2017, 2023

Offset: 1

J. Lowell, May 17 2014

Includes all years starting on Sunday and leap years starting on Saturday.

"The Gregorian calendar has been in use in the Western world since 1582 by Roman Catholic countries and since 1752 by English speaking countries." The Mathematica Book.

F. Campbell, Leap years with 53 Sundays, Popular Astronomy, 1917, Vol. 25, p.72
Index entries for sequences related to calendars

Cf. A224945, A224951. (Leap years are in those sequences)

Cf. A119406.

cp's OEIS Frontend

A141287 Years in which there are five Fridays in the month of February.

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A135795 Years in which there are five Mondays in the month of February.

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A141039 Years in which there are five Wednesdays in the month of February.

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A143994 Years in which there are five Tuesdays in the month of February.

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A143995 Years in which there are five Thursdays in the month of February, in the Gregorian calendar.

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A176478 Years in which there are five Saturdays in the month of February.

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A174431 Day of the week occurring 5 times in February, or 0 if no such day exists (1 to 7 are Sunday to Saturday).

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A242539 Years with 53 sundays in the Gregorian calendar.

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