OFFSET
1,2
COMMENTS
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.
See A189916 for leap years.
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.
If one uses 0->A, 1->B, 2->C, 3->D, 4->E, 5->F and 6->G the sequence becomes
A, D, D, G, B, E, G, C, F, A, D, F.
A mnemonic rhyme for this sequence is in English:
At Dover dwells George Brown, Esquire,
Good Christopher Fitch and David Frier.
In German (attributed to Thomas Brown, Oxford):
Allvater, der du gnaedig bist,
Ein gesetzestreuer Christ
Fordert Ablauf dieser Frist.
See the L. Holford-Strevens reference pp. 106-7 (German translation).
REFERENCES
L. Holford-Strevens, The History of Time. A Very Short Introduction, Oxford University Press, 2005.
L. Holford-Strevens, Kleine Geschichte der Zeitrechnung und des Kalenders, Reclams Universalbibliothek Nr.18483, Stuttgart, 2008 (German translation).
FORMULA
EXAMPLE
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.
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).
CROSSREFS
KEYWORD
nonn,easy,fini,full
AUTHOR
Wolfdieter Lang, May 02 2011
STATUS
approved