login
A231003
Number of years after which it is not possible to have a date falling on the same day of the week, in the Julian calendar.
1
1, 2, 3, 4, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 24, 25, 26, 27, 29, 30, 31, 32, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 65, 66, 68, 69, 70, 71, 72, 74, 75, 76, 77, 80, 81, 82, 83, 85, 86, 87, 88, 91, 92, 93, 94, 96, 97
OFFSET
1,2
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 28.
This is the complement of A231000.
LINKS
Time And Date, Repeating Calendar
Time And Date, Julian Calendar
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
FORMULA
From Chai Wah Wu, Jun 04 2024: (Start)
a(n) = a(n-1) + a(n-21) - a(n-22) for n > 22.
G.f.: x*(x^21 + x^20 + x^19 + x^18 + 3*x^17 + x^16 + x^15 + x^14 + 2*x^13 + x^12 + x^11 + x^10 + x^9 + 2*x^8 + x^7 + x^6 + x^5 + 3*x^4 + x^3 + x^2 + x + 1)/(x^22 - x^21 - x + 1). (End)
PROG
(PARI) for(i=0, 420, j=0; for(y=0, 420, if(((5*(y\4)+(y%4))%7)==((5*((y+i)\4)+((y+i)%4))%7), j=1)); if(j==0, print1(i", ")))
CROSSREFS
Cf. A230998 (Gregorian calendar).
Sequence in context: A305441 A121405 A330217 * A171551 A096199 A104576
KEYWORD
nonn,easy
AUTHOR
Aswini Vaidyanathan, Nov 02 2013
STATUS
approved