# What is the next integer in this sequence?

First, I offer you a little something to put you in the right spirits:
For many many years, black cats have had some interesting associations and reputations,
which no doubt helped inspire The Black Cat, a short story by Edgar Allan Poe.
Reading it, even fully and carefully, won't help you in solving the puzzle, but it's classic Poe — so indulge yourself!

### Now on to the puzzle!

Here is a set of integers, which share a common property. There are integers both less than the first one listed, and greater than the last, which also share this property; however, between the first and last numbers which appear in this list, there are no values with this property missing from the list. That is, in this range of values, the set of values with the relevant property is presented here in its entirety. $$\dots, 1752, 1758, 1769, 1775, 1780, 1786, 1797, 1809, 1815, 1820, 1826, 1837, 1843, 1848, 1854, 1865, 1871, 1876, 1882, 1893, 1899, 1905, 1911, 1916, 1922, 1933, 1939, 1944, 1950, 1961, 1967, 1972, 1978, 1989, 1995, 2000, 2006, 2017, \dots$$ Your challenge is to identify the property that these integers share, and
give the next entry in the sequence!

Hint:

Do horror movies make for good date nights?

________

Rest assured that I know What (Not) To Do in a Number Sequence Puzzle. I believe I've teased with enough information in setting this sequence puzzle that it is solvable, uniquely, given what I've provided — though the solution will not be obvious. Hints will be added, if (...as) needed.

• I'm not a whit (or at least I don't consider myself to be...) - does that mean reading the poem will help me? – boboquack May 20 '17 at 8:49
• CSV, for those who want to analyse. – boboquack May 20 '17 at 9:06
• "Please see Number-Sequence Puzzles: What (Not) To Do" :P – Beastly Gerbil May 20 '17 at 10:34
• Everyone's a critic ... ;) – Rubio May 20 '17 at 17:49

As the numbers mostly seem to follow a pattern of

differences of 11, 6, 5, 6 repeated,

I initially guessed at

2023

I also believed the numbers refer to

years,

I then noticed that

The regular cycle adds up to 28 and involves 4 numbers in every 28

But that the pattern is messed up around

Century years not divisible by 400

Which made me think of the

Gregorian calendar (which was introduced in 1752!)

On investigation I confirmed that these numbers are

Years in which Christmas day fell on a Monday (or any equivalent property for a date not in January or February, such as ending on a Sunday)

Equivalently,

Years in which October 13 falls on a Friday. Friday 13 October 1307 is one supposed origin of the superstition of Friday the 13th, on this date King Philip IV of France supposedly ordered the elimination of the Knights Templar. It is also a Friday 13th in the same month as Halloween which may somehow make it scarier. In these years Halloween itself falls on a Tuesday which is probably not significant.

And indeed the next such number is

2023

• The property you've found is true, and its corollary "any equivalent property" is both true and relevant. There's a particular one more in keeping with the mood set by the puzzle intro, a peculiarity that hopefully you can find ... – Rubio May 20 '17 at 9:15
• @Rubio intriguing, I'm going to read the Poe story after all! – IanF1 May 20 '17 at 9:19
• @Rubio I added another equivalent, but I don't know if it's what you had in mind... – IanF1 May 20 '17 at 9:25
• So this strayed unintentionally far into "what am I thinking of" territory; I've adjusted the puzzle intro slightly and added a hint that should point the way more clearly. – Rubio May 20 '17 at 9:48
• @Rubio I've added another guess at an "appropriate" equivalent but I still feel like I'm grasping at straws :-) – IanF1 May 20 '17 at 10:02