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Calendar for Sequence of the Day in December
Calendar for Sequence of the Day in November * Calendar for Sequence of the Day in January
Template:Sequence of the Day for December 1 A188892: Numbers such that there is no triangular gonal number greater than 1.
The triangular numbers are essentially the building blocks of the other figurate numbers. Therefore it is rather surprising that there can be sequences of gonal numbers that don't overlap with the sequence of triangular numbers at all (other than 0 and 1.) T. D. Noe has demonstrated that the equation has no integer solutions , as conversion to a generalized Pell equation shows that if , then the first equation has only a finite number of solutions. From there one can pinpoint those values of that produce no integer solutions greater than 1.

Template:Sequence of the Day for December 2 A1202345: Sequence name.
A sentence or two about this sequence.

Template:Sequence of the Day for December 3 A076512 / A109395: , where is the number of distinct prime factors function. The denominator is (the greatest prime factor) if and only if for every , there is a such that .

Template:Sequence of the Day for December 4 A029908: Starting with repeatedly sum prime factors (with multiplicity) until reaching 0 or a fixed point.
The Integer log of n (sum of prime factors of n (with multiplicity)) amounts to replacing multiplication by addition and exponentiation by multiplication in the canonical prime factorization of . Because sopfr(n) <= n (with equality at 4 and the primes), the first appearance of all primes is in the natural order: 2,3,5,7,11,... . [Zak Seidov, Mar 14 2011]

Template:Sequence of the Day for December 5 A197723: Decimal expansion of .
Multiplying a number by (with being the imaginary unit ) is equivalent to rotating it by this amount on the complex plane, which as radians, works out to 270 degrees or 300 gradians.

Template:Sequence of the Day for December 6 A1202345: Sequence name.
A sentence or two about this sequence.
 
Template:Sequence of the Day for December 7 A1202345: Sequence name.
A sentence or two about this sequence.

Template:Sequence of the Day for December 8 A010466: Decimal expansion of .
This is the second Lagrange number, used in the Hurwitz irrational number theorem to obtain very good rational approximations of irrational numbers other than multiples of the golden ratio.

Template:Sequence of the Day for December 9 A1202345: Sequence name.
A sentence or two about this sequence.

Template:Sequence of the Day for December 10 A001190: WedderburnEtherington numbers: binary rooted trees (every node has outdegree 0 or 2) with endpoints (and nodes in all).
This is also the number of ways to place stars in a single bound stable hierarchical multiple star system; i.e. taking only the configurations from A003214 where all stars are included in single outer parentheses.

Template:Sequence of the Day for December 11 A188859: Decimal expansion of .
This is the limit (as increases without bound) of the probability that is less than , with chosen uniformly at random from . (As usual, .)

Template:Sequence of the Day for December 12 A033880: Abundance of .
The negative in this listing correspond to deficient numbers, the zeros correspond to perfect numbers and the positives correspond to abundant numbers. I'm choosing to start the listing here from 27 in order to get a better mix of abundant, perfect and deficient numbers.

Template:Sequence of the Day for December 13 A033879: Deficiency of .
The negative in this listing correspond to abundant numbers, the zeros correspond to perfect numbers and the positives correspond to deficient numbers. I'm choosing to start the listing here from 27 in order to get a better mix of abundant, perfect and deficient numbers.
 
Template:Sequence of the Day for December 14 A1202345: Sequence name.
A sentence or two about this sequence.

Template:Sequence of the Day for December 15 A1202345: Sequence name.
A sentence or two about this sequence.

Template:Sequence of the Day for December 16 A054245: Beethoven's Symphony No. 5 in C minor.
Contrary to popular belief, the first movement of Beethoven's Fifth Symphony has an eightnote motif, not four notes. Here of course we have just the principal melody line, without the bass line and inner voices. Before "polyphonic" ring tones became available, this is how you would hear it as a ring tone. Compare:
Today is Beethoven's birthday, by the way.

Template:Sequence of the Day for December 17 A1202345: Sequence name.
A sentence or two about this sequence.

Template:Sequence of the Day for December 18 A1202345: Sequence name
A sentence or two about this sequence.

Template:Sequence of the Day for December 19 A1202345: Sequence name
A sentence or two about this sequence.

Template:Sequence of the Day for December 20 A119524: Decimal expansion of the van der WaerdenUlam binary measure of the composites.
The formula is , where is the prime counting function. The primes have a larger measure than the composites because they dominate the smaller integers.
 
Template:Sequence of the Day for December 21 A081244: Named periods in the Mayan/mesoamerican calendars.
The periods are named kin, winal, Tzolkin year, tun, Haab year, katun, Calendar Round, baktun, pictun, calabtun, kinchiltun, alautun. With approximately 63 million years, the alautun is probably the longest named period in any calendar. December 21, 2012 marked the end of the 13th baktun, causing some concern over the widely misunderstood prophesied descent of the god of war. But the tablet inscribed with that prophecy is incomplete, so we don't know what, if anything, the Mayans expected the god of war to do upon his descent.

Template:Sequence of the Day for December 22 A1202345: Sequence name
A sentence or two about this sequence.

Template:Sequence of the Day for December 23 A038772: Numbers not divisible by any of their base 10 digits.
All prime numbers with more than one digit and none of those digits 1 are in this sequence.

Template:Sequence of the Day for December 24 A1202345: Sequence name
A sentence or two about this sequence.

Template:Sequence of the Day for December 25
On the first day of Christmas, my true love gave me a partridge in a pear tree. The next day, she gave me two turtle doves and another partridge in a pear tree. And the next day, three French hens, another two turtle doves and yet another partridge in a pear tree. By the seventh day, I had a serious storage problem. If there was a way to encase all these gifts into small balls with a radius of half a unit, a triangular frame with each side twelve units long would be sufficient to organize all these gifts into a nice, little tetrahedron, since it just so happens that the running total of gifts received each day is a tetrahedral number. But of course the whole issue of storage is moot because the gifts are symbols of various concepts relevant to the celebration of Christmas.

Template:Sequence of the Day for December 26 A1202345: Sequence name
A sentence or two about this sequence.

Template:Sequence of the Day for December 27 A151542: Generalized pentagonal numbers:
Originally, pentagonal numbers are those of the form . Those with the "+" sign are sometimes referred to as the "second" pentagonal numbers. The generalized pentagonal numbers , for = 1 through 12, form sequences A000326, A005449, A045943, A115067, A140090, A140091, A059845, A140672, A140673, A140674, A140675, A151542. One might wonder whether it is a pure coincidence to find many "remarkable" numbers in this sequence: multiples of 11 (as 66, 297, 495,...) and other numbers with doubled digits (117, 255 = 2^81 and its reversal 552, 441 and 882, 1116, 1200, 1377, 1566 and its "permutation" 1665, 2205, 2322, 2442, 3225, 3366, ...), the pair 147 and 741; 216 = 6^3, etc...
 
Template:Sequence of the Day for December 28 A1202345: Sequence name
A sentence or two about this sequence.

Template:Sequence of the Day for December 29 A1202345: Sequence name
A sentence or two about this sequence.

Template:Sequence of the Day for December 30 A202138/A203363: The numbers of Conway's PRIMEGAME
It's a bit of a rollercoaster, but these numbers generate prime numbers.

Template:Sequence of the Day for December 31 A1202345: Sequence name
A sentence or two about this sequence.
