A143994 -id:A143994 - 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

A119406 Years in which there are five Sundays in the month of February.

Original entry on oeis.org

1756, 1784, 1824, 1852, 1880, 1920, 1948, 1976, 2004, 2032, 2060, 2088, 2128, 2156, 2184, 2224, 2252, 2280, 2320, 2348, 2376, 2404, 2432, 2460, 2488, 2528, 2556, 2584, 2624, 2652, 2680, 2720, 2748, 2776, 2804, 2832, 2860, 2888, 2928, 2956, 2984, 3024

Offset: 1

George G. Szpiro (george(AT)netvision.net.il) and Robert G. Wilson v, Jul 05 2006

"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 Gregorian calendar counts leap years every year divisible by 4, except for centuries not divisible by 400, which are not leap years." - The Mathematica Book

Because the days of the week of the Gregorian calendar repeat every 400 years, the first differences of this sequence have period 13: [28, 40, 28, 28, 40, 28, 28, 28, 28, 28, 28, 40, 28]. - Nathaniel Johnston, May 30 2011

George G. Szpiro, The Secret Life Of Numbers, 50 Easy Pieces On How Mathematicians Work And Think, Joseph Henry Press, Washington, D.C., 2006, Chapter 1, "Lopping Leap Years", pages 3-5.

TimeAndDate.com, A calendar website
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. A008685, A011763, A011770.

Cf. A135795 (Mon), A143994 (Tue), A141039 (Wed), A143995 (Thu), A141287 (Fri), A176478 (Sat).

A119406 := proc(n) local s: s:=[0, 28, 68, 96, 124, 164, 192, 220, 248, 276, 304, 332, 372]: return 1756 + 400*floor((n-1)/13) + s[((n-1) mod 13) + 1]: end: seq(A119406(n),n=1..42); # Nathaniel Johnston, May 30 2011

(* first do *) Needs["Miscellaneous`Calendar`"] (* then *) fQ[y_] := Mod[y, 4] == 0 && Mod[y, 400] ? 0 && DayOfWeek[{y, 2, 1}] == Sunday; Select[ Range[1582, 3051], fQ@# &]
(* Second program, needing Mma version >= 9.0 *)
okQ[y_] := Mod[y, 4] == 0 && DayCount[{y, 1, 31}, DatePlus[{y, 3, 1}, -1], Sunday] == 5;
Select[Range[1752, 3051, 4], okQ] (* Jean-François Alcover, Mar 27 2020 *)

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

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

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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A119406 Years in which there are five Sundays 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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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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