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.

A224945 Leap years having 53 Sundays and Mondays.

Original entry on oeis.org

1584, 1612, 1640, 1668, 1696, 1708, 1736, 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
Offset: 1

Views

Author

Aswini Vaidyanathan, Apr 21 2013

Keywords

Comments

Gregorian calendar repeats after every 400 years because number of days in 400 years is 146097 which is a multiple of 7.
Non-century years are leap years if and only if they are multiples of 4 while century years are leap years if and only if they are multiples of 400.
15 occurrences in 400 years.
Months having Friday the 13th: January, April and July.
February 29th falls on Wednesday.
366 day leap year: 53 Sundays, 53 Mondays, 52 Tuesdays, 52 Wednesdays, 52 Thursdays, 52 Fridays, 52 Saturdays.

Links

Crossrefs

Cf. A224946, A224947, A224948, A224949, A224950, A224951.

Programs

  • Mathematica
    Needs["Calendar`"]; Select[Range[1583, 2800], DayOfWeek[{#, 1, 1}, Calendar -> Gregorian] == Sunday && DaysBetween[{#, 1, 1}, {# + 1, 1, 1}, Calendar -> Gregorian] == 366 &, 50] (* T. D. Noe, Apr 22 2013 *)
Select[Range[1583,3000],LeapYearQ[{#}]&&DayName[{#,1,1}]==Sunday&] (* Harvey P. Dale, Jul 04 2018, v9 or later *)

A224951 Leap years having 53 Saturdays and Sundays.

Original entry on oeis.org

1600, 1628, 1656, 1684, 1724, 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
Offset: 1

Views

Author

Aswini Vaidyanathan, Apr 21 2013

Keywords

Comments

Gregorian calendar repeats after every 400 years because number of days in 400 years is 146097 which is a multiple of 7.
Non-century years are leap years if and only if they are multiples of 4 while century years are leap years if and only if they are multiples of 400.
13 occurrences in 400 years.
Months having Friday the 13th: October.
February 29th falls on Tuesday.
366 day leap year: 53 Sundays, 52 Mondays, 52 Tuesdays, 52 Wednesdays, 52 Thursdays, 52 Fridays, 53 Saturdays.

Links

Crossrefs

Cf. A224945, A224946, A224947, A224948, A224949, A224950.

Programs

  • Mathematica
    Needs["Calendar`"]; Select[Range[1583, 2800], DayOfWeek[{#, 1, 1}, Calendar -> Gregorian] == Saturday && DaysBetween[{#, 1, 1}, {# + 1, 1, 1}, Calendar -> Gregorian] == 366 &, 50] (* T. D. Noe, Apr 22 2013 *)
Select[Range[1583,3000],LeapYearQ[{#}]&&DayName[{#,1,1}]==Saturday&] (* Ray Chandler, Jul 26 2023, v9 or later, after Harvey P.Dale at A224945 *)

A224946 Leap years having 53 Mondays and Tuesdays.

Original entry on oeis.org

1596, 1624, 1652, 1680, 1720, 1748, 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
Offset: 1

Views

Author

Aswini Vaidyanathan, Apr 21 2013

Keywords

Comments

Gregorian calendar repeats after every 400 years because number of days in 400 years is 146097 which is a multiple of 7.
Non-century years are leap years if and only if they are multiples of 4 while century years are leap years if and only if they are multiples of 400.
13 occurrences in 400 years.
Months having Friday the 13th: September and December.
February 29th falls on Thursday.
366 day leap year: 52 Sundays, 53 Mondays, 53 Tuesdays, 52 Wednesdays, 52 Thursdays, 52 Fridays, 52 Saturdays.

Links

Crossrefs

Cf. A224945, A224947, A224948, A224949, A224950, A224951.

Programs

  • Mathematica
    Needs["Calendar`"]; Select[Range[1583, 2800], DayOfWeek[{#, 1, 1}, Calendar -> Gregorian] == Monday && DaysBetween[{#, 1, 1}, {# + 1, 1, 1}, Calendar -> Gregorian] == 366 &, 50] (* T. D. Noe, Apr 22 2013 *)
Select[Range[1583,3000],LeapYearQ[{#}]&&DayName[{#,1,1}]==Monday&] (* Ray Chandler, Jul 26 2023, v9 or later, after Harvey P.Dale at A224945 *)

A224948 Leap years having 53 Wednesdays and Thursdays.

Original entry on oeis.org

1592, 1620, 1648, 1676, 1716, 1744, 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
Offset: 1

Views

Author

Aswini Vaidyanathan, Apr 21 2013

Keywords

Comments

Gregorian calendar repeats after every 400 years because number of days in 400 years is 146097 which is a multiple of 7.
Non-century years are leap years if and only if they are multiples of 4 while century years are leap years if and only if they are multiples of 400.
14 occurrences in 400 years.
Months having Friday the 13th: March and November.
February 29th falls on Saturday.
366 day leap year: 52 Sundays, 52 Mondays, 52 Tuesdays, 53 Wednesdays, 53 Thursdays, 52 Fridays, 52 Saturdays.

Links

Crossrefs

Cf. A224945, A224946, A224947, A224949, A224950, A224951.

Programs

  • Mathematica
    Needs["Calendar`"]; Select[Range[1583, 2800], DayOfWeek[{#, 1, 1}, Calendar -> Gregorian] == Wednesday && DaysBetween[{#, 1, 1}, {# + 1, 1, 1}, Calendar -> Gregorian] == 366 &, 50] (* T. D. Noe, Apr 22 2013 *)
Select[Range[1583,3000],LeapYearQ[{#}]&&DayName[{#,1,1}]==Wednesday&] (* Ray Chandler, Jul 26 2023, v9 or later, after Harvey P.Dale at A224945 *)

A224949 Leap years having 53 Thursdays and Fridays.

Original entry on oeis.org

1604, 1632, 1660, 1688, 1728, 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
Offset: 1

Views

Author

Aswini Vaidyanathan, Apr 21 2013

Keywords

Comments

Gregorian calendar repeats after every 400 years because number of days in 400 years is 146097 which is a multiple of 7.
Non-century years are leap years if and only if they are multiples of 4 while century years are leap years if and only if they are multiples of 400.
13 occurrences in 400 years.
Months having Friday the 13th: February and August.
February 29th falls on Sunday.
366 day leap year: 52 Sundays, 52 Mondays, 52 Tuesdays, 52 Wednesdays, 53 Thursdays, 53 Fridays, 52 Saturdays.

Links

Crossrefs

Cf. A224945, A224946, A224947, A224948, A224950, A224951.

Programs

  • Mathematica
    Needs["Calendar`"]; Select[Range[1583, 2800], DayOfWeek[{#, 1, 1}, Calendar -> Gregorian] == Thursday && DaysBetween[{#, 1, 1}, {# + 1, 1, 1}, Calendar -> Gregorian] == 366 &, 50] (* T. D. Noe, Apr 22 2013 *)
Select[Range[1583,3000],LeapYearQ[{#}]&&DayName[{#,1,1}]==Thursday&] (* Ray Chandler, Jul 26 2023, v9 or later, after Harvey P.Dale at A224945 *)

A224950 Leap years having 53 Fridays and Saturdays.

Original entry on oeis.org

1588, 1616, 1644, 1672, 1712, 1740, 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
Offset: 1

Views

Author

Aswini Vaidyanathan, Apr 21 2013

Keywords

Comments

Gregorian calendar repeats after every 400 years because number of days in 400 years is 146097 which is a multiple of 7.
Non-century years are leap years if and only if they are multiples of 4 while century years are leap years if and only if they are multiples of 400.
15 occurrences in 400 years.
Months having Friday the 13th: May.
February 29th falls on Monday.
366 day leap year: 52 Sundays, 52 Mondays, 52 Tuesdays, 52 Wednesdays, 52 Thursdays, 53 Fridays, 53 Saturdays.

Links

Crossrefs

Cf. A224945, A224946, A224947, A224948, A224949, A224951.

Programs

  • Mathematica
    Needs["Calendar`"]; Select[Range[1583, 2800], DayOfWeek[{#, 1, 1}, Calendar -> Gregorian] == Friday && DaysBetween[{#, 1, 1}, {# + 1, 1, 1}, Calendar -> Gregorian] == 366 &, 50] (* T. D. Noe, Apr 22 2013 *)
ly53Q[y_]:=LeapYearQ[{y}]&&Count[DayRange[{y,1,1},{y,12,31}],?(DayName[ #]==Friday&)]==53&&Count[DayRange[{y,1,1},{y,12,31}],?(DayName[#] == Saturday&)] ==53; Select[Range[1570,2800],ly53Q] (* Harvey P. Dale, Oct 14 2021, v9 or later *)
Showing 1-6 of 6 results.

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