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A230997
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Number of years after which it is possible to have a date falling on same day of the week, but the entire year does not have the same calendar, in the Gregorian calendar.
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2
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5, 7, 33, 35, 61, 63, 89, 91, 117, 131, 145, 159, 173, 187, 213, 227, 241, 255, 269, 283, 309, 311, 337, 339, 365, 367, 393, 395, 405, 407, 433, 435, 461, 463, 489, 491, 517, 531, 545, 559, 573, 587, 613, 627, 641, 655, 669, 683, 709, 711, 737, 739, 765, 767, 793, 795
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OFFSET
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1,1
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COMMENTS
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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 400.
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LINKS
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EXAMPLE
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5 belongs to this sequence because January 1, 2012 falls on same day as January 1, 2017 but the calendar is not completely the same for both the years. In fact, a difference of 5 years can never produce the same calendar for the entire year.
7 belongs to this sequence because January 1, 2097 falls on same day as January 1, 2104 but the calendar is not completely the same for both the years. In fact, a difference of 7 years can never produce the same calendar for the entire year.
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PROG
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(PARI) for(i=0, 400, j=0; for(y=0, 400, if(((5*(y\4)+(y%4)-(y\100)+(y\400))%7)==((5*((y+i)\4)+((y+i)%4)-((y+i)\100)+((y+i)\400))%7), j=1; break)); for(y=0, 400, if(((5*(y\4)+(y%4)-(y\100)+(y\400))%7)==((5*((y+i)\4)+((y+i)%4)-((y+i)\100)+((y+i)\400))%7)&&((5*(y\4)+(y%4)-(y\100)+(y\400)-!(y%4)+!(y%100)-!(y%400))%7)==((5*((y+i)\4)+((y+i)%4)-((y+i)\100)+((y+i)\400)-!((y+i)%4)+!((y+i)%100)-!((y+i)%400))%7), j=2; break)); if(j==1, print1(i", ")))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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