A231005 Number of months after which a date can fall on the same day of the week, in the Gregorian calendar.

0, 1, 3, 6, 8, 9, 11, 14, 15, 17, 18, 19, 20, 22, 23, 26, 27, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 45, 46, 49, 50, 52, 53, 54, 55, 57, 58, 60, 61, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 91, 92, 94, 95, 98, 99

Offset: 0

Author

Aswini Vaidyanathan, Nov 02 2013

Keywords

• nonn
• easy

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.

Examples

			1 belongs to this sequence because February 1, 2013 falls on the same day as March 1, 2013.
3 belongs to this sequence because December 1, 2011 falls on the same day as March 1, 2012.
6 belongs to this sequence because January 1, 2012 falls on the same day as July 1, 2012.
8 belongs to this sequence because March 1, 2013 falls on the same day as November 1, 2013.
9 belongs to this sequence because January 1, 2013 falls on the same day as October 1, 2013.
11 belongs to this sequence because December 1, 2011 falls on the same day as November 1, 2012.
		

Links

• Time And Date, Repeating Months
• Time And Date, Gregorian Calendar

Crossrefs

Cf. A230995-A231014.

Cf. A231010 (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],print1(p", ");break)))