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A131773 Epact in Julian calendar for a year n with Golden Number (n mod 19) + 1 = A074805(n).

%I A131773 #10 Sep 14 2019 15:47:29
%S A131773 30,11,22,3,14,25,6,17,28,9,20,1,12,23,4,15,26,7,18,30,11,22,3,14,25,
%T A131773 6,17,28,9,20,1,12,23,4,15,26,7,18,30,11,22,3,14,25,6,17,28,9,20,1,12,
%U A131773 23,4,15,26,7,18,30,11,22,3,14,25,6,17,28,9,20,1,12,23,4,15,26,7,18,30,11
%N A131773 Epact in Julian calendar for a year n with Golden Number (n mod 19) + 1 = A074805(n).
%C A131773 Periodic with period 19 as there are 19 Golden Numbers. Basis for calculating Gregorian Epact. See sections about Epacts, Golden Numbers and discussion of the 19-year Metonic cycle (in Chapter 1) of the Calendar FAQ link. The FAQ also discusses in detail in which years the different calendars have been adopted by different countries and that there was no year 0 (unless considering, say, a "proleptic" Gregorian calendar) -- so the first term here (and in A074805) is actually for 1 BC (1 BCE) of the Julian calendar.
%H A131773 Claus Tondering, <a href="http://www.tondering.dk/claus/calendar.html">Frequently Asked Questions about Calendars</a>.
%H A131773 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).
%F A131773 a(n) = (11*(A074805(n)-1)) mod 30, but replacing every 0 result with 30. See program and link.
%F A131773 G.f.: (18*x^18 +7*x^17 +26*x^16 +15*x^15 +4*x^14 +23*x^13 +12*x^12 +x^11 +20*x^10 +9*x^9 +28*x^8 +17*x^7 +6*x^6 +25*x^5 +14*x^4 +3*x^3 +22*x^2 +11*x +30)/(-x^19 +1). - _Colin Barker_, Jul 18 2013
%e A131773 a(2007)=12 as the Julian Epact for the year 2007 is (11*(2007 mod 19)) mod 30 = (11*12) mod 30 = 12. ((2007 mod 19)+1 = 12+1 = 13 = A074805(2007) is the corresponding Golden Number for 2007).
%t A131773 LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},{30, 11, 22, 3, 14, 25, 6, 17, 28, 9, 20, 1, 12, 23, 4, 15, 26, 7, 18},78] (* _Ray Chandler_, Aug 27 2015 *)
%t A131773 PadRight[{},120,{30,11,22,3,14,25,6,17,28,9,20,1,12,23,4,15,26,7,18}] (* _Harvey P. Dale_, Sep 14 2019 *)
%o A131773 (PARI) a(n)= JE=(11*(n%19))%30; if(JE==0,30,JE)
%Y A131773 Cf. A074805.
%K A131773 nonn,easy
%O A131773 0,1
%A A131773 _Rick L. Shepherd_, Jul 14 2007