A231000 Number of years after which a date can fall on the same day of the week, in the Julian calendar.

0, 5, 6, 11, 17, 22, 23, 28, 33, 34, 39, 45, 50, 51, 56, 61, 62, 67, 73, 78, 79, 84, 89, 90, 95, 101, 106, 107, 112, 117, 118, 123, 129, 134, 135, 140, 145, 146, 151, 157, 162, 163, 168, 173, 174, 179, 185, 190, 191, 196, 201, 202, 207, 213, 218, 219, 224, 229, 230, 235

Offset

0,2

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.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Time And Date, Repeating Calendar

Time And Date, Julian Calendar

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).

Formula

From Colin Barker, Oct 17 2019: (Start)

G.f.: x*(1 - x + x^2)*(5 + 6*x + 6*x^2 + 6*x^3 + 5*x^4) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).

a(n) = a(n-1) + a(n-7) - a(n-8) for n>7.

(End)

Prog

(PARI) for(i=0, 420, for(y=0, 420, if(((5*(y\4)+(y%4))%7)==((5*((y+i)\4)+((y+i)%4))%7), print1(i", "); break)))
(PARI) concat(0, Vec(x*(1 - x + x^2)*(5 + 6*x + 6*x^2 + 6*x^3 + 5*x^4) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)) + O(x^40))) \\ Colin Barker, Oct 17 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); [0] cat Coefficients(R!( x*(1-x+x^2)*(5+6*x+6*x^2+6*x^3+5*x^4)/((1-x)^2*(1+x+x^2+x^3+x^4+x^5+x^6)) )); // Marius A. Burtea, Oct 17 2019

Crossrefs

Cf. A230995-A231014.

Cf. A230995 (Gregorian calendar).

Sequence in context: A101187 A277550 A070373 * A274283 A022095 A042531

Adjacent sequences: A230997 A230998 A230999 * A231001 A231002 A231003

Keyword

nonn,easy

Author

Aswini Vaidyanathan, Nov 02 2013

Status

approved