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 1-3 of 3 results.

A231014 Number of months after which it is not possible to have the same calendar for the entire month with the same number of days, in the Julian calendar.

Original entry on oeis.org

1, 2, 4, 5, 7, 10, 11, 12, 13, 16, 19, 21, 24, 25, 27, 28, 30, 33, 36, 39, 41, 42, 44, 45, 47, 48, 49, 50, 51, 53, 56, 58, 59, 61, 62, 65, 66, 67, 70, 71, 73, 74, 76, 79, 82, 83, 84, 85, 87, 88, 90, 91, 93, 96, 97, 99, 100, 102, 104, 105, 107, 108, 111, 113, 116, 119, 120
Offset: 1

Views

Author

Aswini Vaidyanathan, Nov 02 2013

Keywords

Comments

In the Julian calendar, a year is a leap year if and only if it is a multiple of 4 and all century years are leap years.
Assuming this fact, this sequence is periodic with a period of 336.
This is the complement of A231011.

Links

Crossrefs

Cf. A230995-A231014.
Cf. A231009 (Gregorian calendar).

Programs

  • PARI
    m=[0,3,3,6,1,4,6,2,5,0,3,5];n=[31,28,31,30,31,30,31,31,30,31,30,31];y=vector(336,i,(m[((i-1)%12)+1]+((5*((i-1)\48)+(((i-1)\12)%4)-!((i-1)%48)-!((i-2)%48))))%7);x=vector(336,i,n[((i-1)%12)+1]+!((i-2)%48));for(p=0,336,j=0;for(q=0,336,if(y[(q%336)+1]==y[((q+p)%336)+1]&&x[(q%336)+1]==x[((q+p)%336)+1],j=1;break));if(j==0,print1(p", ")))

A231006 Number of months after which a date can fall on the same day of the week, and the two months can have the same number of days, in the Gregorian calendar.

Original entry on oeis.org

0, 3, 6, 8, 9, 14, 15, 17, 18, 20, 22, 23, 26, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 46, 49, 50, 52, 54, 55, 57, 58, 60, 63, 64, 66, 67, 68, 69, 72, 75, 76, 77, 78, 80, 81, 84, 86, 87, 89, 90, 92, 94, 95, 98, 101, 103, 104, 106, 107, 109, 110, 112, 113, 114, 115, 117, 118
Offset: 0

Views

Author

Aswini Vaidyanathan, Nov 02 2013

Keywords

Comments

In the Gregorian calendar, a non-century year is a leap year if and only if it is a multiple of 4 and a century year is a leap year if and only if it is a multiple of 400.
Assuming this fact, this sequence is periodic with a period of 4800.
This is a subsequence of A231005.

Examples

			3 belongs to this sequence because December 1, 2011 falls on the same day as March 1, 2012 and both December and March have 31 days each.
6 belongs to this sequence because January 1, 2012 falls on the same day as July 1, 2012 and both January and July have 31 days each.
8 belongs to this sequence because May 1, 2013 falls on the same day as January 1, 2014 and both May and January have 31 days each.
9 belongs to this sequence because January 1, 2013 falls on the same day as October 1, 2013 and both January and October have 31 days each.

Links

Crossrefs

Cf. A230995-A231014.
Cf. A231011 (Julian calendar).

Programs

  • PARI
    m=[0,3,3,6,1,4,6,2,5,0,3,5];n=[31,28,31,30,31,30,31,31,30,31,30,31];y=vector(4800,i,(m[((i-1)%12)+1]+((5*((i-1)\48)+(((i-1)\12)%4)-((i-1)\1200)+((i-1)\4800)-!((i-1)%48)+!((i-1)%1200)-!((i-1)%4800)-!((i-2)%48)+!((i-2)%1200)-!((i-2)%4800))))%7);x=vector(4800,i,n[((i-1)%12)+1]+!((i-2)%48)-!((i-2)%1200)+!((i-2)%4800));for(p=0,4800,for(q=0,4800,if(y[(q%4800)+1]==y[((q+p)%4800)+1]&&x[(q%4800)+1]==x[((q+p)%4800)+1],print1(p", ");break)))

A231012 Number of months after which a date can fall on the same day of the week, but it is not possible that the two months have the same number of days, in the Julian calendar.

Original entry on oeis.org

1, 11, 19, 27, 28, 41, 45, 49, 58, 61, 66, 71, 73, 74, 83, 87, 91, 100, 104, 113, 121, 130, 131, 133, 138, 143, 146, 159, 160, 176, 177, 190, 193, 198, 203, 205, 206, 215, 223, 232, 236, 245, 249, 253, 262, 263, 265, 270, 275, 278, 287, 291, 295, 308, 309, 317, 325, 335
Offset: 1

Views

Author

Aswini Vaidyanathan, Nov 02 2013

Keywords

Comments

In the Julian calendar, a year is a leap year if and only if it is a multiple of 4 and all century years are leap years.
Assuming this fact, this sequence is periodic with a period of 336.
These are the terms of A231010 not in A231011.

Links

Crossrefs

Cf. A230995-A231014.
Cf. A231007 (Gregorian calendar).

Programs

  • PARI
    m=[0,3,3,6,1,4,6,2,5,0,3,5];n=[31,28,31,30,31,30,31,31,30,31,30,31];y=vector(336,i,(m[((i-1)%12)+1]+((5*((i-1)\48)+(((i-1)\12)%4)-!((i-1)%48)-!((i-2)%48))))%7);x=vector(336,i,n[((i-1)%12)+1]+!((i-2)%48));for(p=0,336,j=0;for(q=0,336,if(y[(q%336)+1]==y[((q+p)%336)+1],j=1;break));for(q=0,336,if(y[(q%336)+1]==y[((q+p)%336)+1]&&x[(q%336)+1]==x[((q+p)%336)+1],j=2;break));if(j==1,print1(p", ")))
Showing 1-3 of 3 results.

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