cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A178055 Numbers representing the number of days in a month in the Gregorian calendar (modulus 7).

Original entry on oeis.org

3, 1, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 0, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 0, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 0, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 1, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 0, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 0, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 0, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 3, 1, 3, 2, 3, 2, 3, 3, 2
Offset: 1

Views

Author

Lyle P. Blosser (lyleblosser(AT)att.net), May 18 2010

Keywords

Comments

Sequence first term represents January 2000. Sequence repeats after 4800 terms, representing 400 years in the Gregorian calendar system.
Actual number of days in a month can be determined by adding 28 to the value of the sequence term representing the month in question.

Examples

			a(1) = 3 -> January 2000 has 31 days (3+28), a(2) = 1 -> February 2000 has 29 days (1+28), a(3) = 3 -> March 2000 has 31 days (3+28).

Links

Crossrefs

Cf. A178054. If a(n) is the n-th term in A178054 and b(n) is the n-th term in A178055, then a(n) + b(n) (modulus 7) = a(n+1)

Programs

  • Mathematica
    dys[{y_,m_,1}]:=If[m==12,DateDifference[{y,m,1},{y+1,1,1}],DateDifference[ {y,m,1},{y,m+1,1}]][[1]]; Mod[#,7]&/@(dys/@ Flatten[Table[{y,m,1},{y,2000,2010},{m,12}],1])  (* Harvey P. Dale, Sep 04 2020 *)

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

Views

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.

A189916 Sequence for finding the day of the week for the first day of the month in leap years.

Original entry on oeis.org

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

Views

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 leap years. Remember that the year 2000 was a leap year. See A189915 for non-leap years.
If Jan 01 falls on a day of the week with index I, then Feb 01 falls on the day with index I+3 (mod 7), Mar 01 falls on the day with index I+4 (mod 7), Apr 01 is again on the day with index I, etc.
If one uses 0->A, 1->B, 2->C, 3->D, 4->E, 5->F and 6->G then the sequence becomes A, D, E, A, C, F, A, D, G, B, E, G.

Examples

			In the year 2008 Jan 01 has index 2 (Tuesday). Therefore, Feb 01 has index 2+3 = 5 (mod 7) (Friday), Mar 01 has index 2+4 = 6 (mod 7) (Saturday), Apr 01 falls again on a Tuesday, May 01 has index 2+2 = 4 (Thursday), Jun 01 has index 2+5= 0 (mod 7) (Sunday). Jul 01 falls again on Tuesday, etc.
For leap years in which Jan 01 has index 0 (Sunday) the pattern for the first days of the months is Sun, Wed, Thu, Sun, Tue, Fri, Sun, Wed, Sat, Mon, Thu, Sat.

References

Crossrefs

Cf. A061251, A178054 (index pattern starting with the year 2000), A189915.

Formula

I(n) = I + a(n) (mod 7), n=1,2,..,12, with I the index of the day of Jan 01 in a leap year, and I(n) the index of the first day the n-th month in this year.
a(n) = A061251(35+n) - 1095 mod(7), n=1..12.
a(n) = A178054(144+n), n=1,...,12 (indices for the year 2012).
Showing 1-3 of 3 results.

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