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A231000 Number of years after which a date can fall on the same day of the week, in the Julian calendar. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 6 03:02 EDT 2020. Contains 335475 sequences. (Running on oeis4.)