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A189915 Sequence for finding the day of the week for the first day of the month in a common (non-leap) year.

%I A189915 #17 Nov 23 2019 04:03:21
%S A189915 0,3,3,6,1,4,6,2,5,0,3,5
%N A189915 Sequence for finding the day of the week for the first day of the month in a common (non-leap) year.
%C A189915 The days of the week, starting with Sunday, have indices 0,1,...,6. The months of the year, starting with January, are numbered 1,2,...,12. The following pattern holds for common (non-leap) years.
%C A189915   See A189916 for leap years.
%C A189915 If Jan 01 falls on a day of the week with index I, then Feb 01 is on the day with index I+3 (mod 7), Mar 01 is also on the day with index I+3 (mod 7), Apr 01 is on the day with index I+6 (mod 7), etc.
%C A189915 If one uses 0->A, 1->B, 2->C, 3->D, 4->E, 5->F and 6->G the sequence becomes
%C A189915   A, D, D, G, B, E, G, C, F, A, D, F.
%C A189915   A mnemonic rhyme for this sequence is in English:
%C A189915   At Dover dwells George Brown, Esquire,
%C A189915   Good Christopher Fitch and David Frier.
%C A189915   In German (attributed to Thomas Brown, Oxford):
%C A189915   Allvater, der du gnaedig bist,
%C A189915   Ein gesetzestreuer Christ
%C A189915   Fordert Ablauf dieser Frist.
%C A189915   See the L. Holford-Strevens reference pp. 106-7 (German translation).
%D A189915 L. Holford-Strevens, The History of Time. A Very Short Introduction, Oxford University Press, 2005.
%D A189915 L. Holford-Strevens, Kleine Geschichte der Zeitrechnung und des Kalenders, Reclams Universalbibliothek Nr.18483, Stuttgart, 2008 (German translation).
%F A189915 I(n) = I + a(n) (mod 7), n=1,...,12, with I the index of January 01 in a common (non-leap) year, and I(n) the index of the day of the week of the first day of the n-th month in this year.
%F A189915 a(n) = A061251(n) (mod 7), n=0,..,11.
%F A189915 a(n) = A178054(72+n), n=1..12.
%e A189915 In the year 2011 Jan 01 has index 6 (Saturday). Therefore, Feb 01 has index 6+3 = 2 (mod 7) (Tuesday), Mar 01 also has index 2, Apr 01 has index 6+6 = 5 (mod 7) (Friday), etc.
%e A189915 In common years with Jan 01 on a Sunday (index 0) the sequence gives the index of the first day of the n-th month of this year. E.g., in the year 2006 (but not in the leap year 2012).
%Y A189915 Cf. A178054 (indices starting with Jan 01 2000), A061251.
%K A189915 nonn,easy,fini,full
%O A189915 1,2
%A A189915 _Wolfdieter Lang_, May 02 2011