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 1-6 of 6 results.

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

Original entry on oeis.org

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

Views

Author

J. Lowell, Aug 01 2008

Keywords

Links

Crossrefs

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

Programs

  • Maple
    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
  • Mathematica
    (* 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 *)

Extensions

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

Views

Author

J. Lowell, Mar 03 2008

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    (* 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 *)

Extensions

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

Views

Author

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

Keywords

Comments

"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

References

  • 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.

Links

Crossrefs

Cf. A008685, A011763, A011770.
Cf. A135795 (Mon), A143994 (Tue), A141039 (Wed), A143995 (Thu), A141287 (Fri), A176478 (Sat).

Programs

  • Maple
    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
  • Mathematica
    (* 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

Views

Author

J. Lowell, Jul 30 2008

Keywords

Links

Crossrefs

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

Programs

  • Maple
    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
  • Mathematica
    (* 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 *)

Extensions

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

Views

Author

J. Lowell, Sep 07 2008

Keywords

Links

Crossrefs

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

Programs

  • Maple
    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
  • Mathematica
    (* 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 *)

Extensions

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

Views

Author

J. Lowell, Sep 07 2008

Keywords

Links

Crossrefs

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

Programs

  • Maple
    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
  • Mathematica
    (* 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 *)

Extensions

More terms from R. J. Mathar, Mar 29 2010
Showing 1-6 of 6 results.

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