A231007 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 Gregorian calendar.

1, 11, 19, 27, 28, 44, 45, 53, 61, 70, 71, 73, 74, 83, 91, 99, 100, 116, 125, 131, 133, 143, 145, 146, 160, 171, 177, 185, 193, 202, 203, 205, 206, 215, 217, 223, 231, 232, 248, 249, 257, 263, 265, 274, 275, 277, 278, 287, 295, 303, 309, 320, 334, 335, 337, 347, 349, 355, 364

Offset

1,2

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.

These are the terms of A231005 not in A231006.

Links

Table of n, a(n) for n=1..59.

Time And Date, Repeating Months

Time And Date, Gregorian Calendar

Example

1 belongs to this sequence because February 1, 2013 falls on the same day as March 1, 2013, but both February and March do not have the same number of days. In fact, a difference of 1 month can never produce the same calendar for the entire month, with the same number of days.
11 belongs to this sequence because December 1, 2011 falls on the same day as November 1, 2012 but both December and November do not have the same number of days. In fact, a difference of 11 months can never produce the same calendar for the entire month, with the same number of days.

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, j=0; for(q=0, 4800, if(y[(q%4800)+1]==y[((q+p)%4800)+1], j=1; break)); for(q=0, 4800, if(y[(q%4800)+1]==y[((q+p)%4800)+1]&&x[(q%4800)+1]==x[((q+p)%4800)+1], j=2; break)); if(j==1, print1(p", ")))

Crossrefs

Cf. A230995-A231014.

Cf. A231012 (Julian calendar).

Sequence in context: A029481 A289700 A231012 * A129916 A032694 A368374

Adjacent sequences: A231004 A231005 A231006 * A231008 A231009 A231010

Keyword

nonn,easy

Author

Aswini Vaidyanathan, Nov 02 2013

Status

approved