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.

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

0,2

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.

Links

Table of n, a(n) for n=0..66.

Time And Date, Repeating Months

Time And Date, Gregorian Calendar

Example

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.

Prog

(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)))

Crossrefs

Cf. A230995-A231014.

Cf. A231011 (Julian calendar).

Sequence in context: A376279 A140516 A310140 * A231011 A196370 A005622

Adjacent sequences: A231003 A231004 A231005 * A231007 A231008 A231009

Keyword

nonn,easy

Author

Aswini Vaidyanathan, Nov 02 2013

Status

approved