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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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.

Original entry on oeis.org

0, 3, 3, 6, 1, 4, 6, 2, 5, 0, 3, 5
Offset: 1

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Author

Wolfdieter Lang, May 02 2011

Keywords

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).

Examples

			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).

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).

Crossrefs

Cf. A178054 (indices starting with Jan 01 2000), A061251.

Formula

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.
a(n) = A061251(n) (mod 7), n=0,..,11.
a(n) = A178054(72+n), n=1..12.
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