A231004 Number of years after which it is not possible to have the same calendar for the entire year, in the Julian calendar.
1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 63, 64, 65, 66, 68, 69, 70, 71, 72, 74, 75, 76, 77, 79, 80, 81, 82, 83, 85, 86, 87
Offset: 1
Links
- Time And Date, Repeating Calendar
- Time And Date, Julian Calendar
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
Programs
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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)&&((5*(y\4)+(y%4)-!(y%4))%7)==((5*((y+i)\4)+((y+i)%4)-!((y+i)%4))%7),j=1));if(j==0,print1(i", ")))
Formula
From Chai Wah Wu, Jun 04 2024: (Start)
a(n) = a(n-1) + a(n-23) - a(n-24) for n > 24.
G.f.: x*(x^23 + x^22 + x^21 + x^20 + x^19 + 2*x^18 + x^17 + x^16 + x^15 + 2*x^14 + x^13 + x^12 + x^11 + x^10 + 2*x^9 + x^8 + x^7 + x^6 + 2*x^5 + x^4 + x^3 + x^2 + x + 1)/(x^24 - x^23 - x + 1). (End)
Comments