When is the next "double-13 Friday"?

[Jonathan Post]

There is a query about the next date in a sequence. Yesterday was such a
date:  double-13 Friday: All the numbers in the numerical notation --
10/13/2006 -- add up to 13 as well.

Dear G.L.,

Should be easy in Mathematica, which I have not yet bought. I guess I'd
start with: A101312 Number of "Friday the 13ths" in year n
(starting at 1901).
2, 1, 3, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 3, 1, 1, 2, 2,
1, 2, 1, 2, 2, 1, 3, 1, 1, 3, 2, 1, 3, 1, 2, 2, 2, 2,
1, 1, 2, 2, 1, 3, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 3, 1,
1, 3, 2, 1, 3, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 3, 1, 1,
2, 2, 1, 2, 1, 2, 2, 1, 3, 1, 1, 3, 2, 1, 3, 1, 2, 2,
2, 2, 1, 1, 2, 2, 1, 3, 1, 1, 2, 2, 1, 2, 1

OFFSET
1901,1

COMMENT

This sequence is basically periodic with period 28
[example: a(1901) = a(1929) = a(1957)], with "jumps"
when it passes a non-leap-year century such as 2100
[all centuries which are not multiples of 400]. At
these points [for example, a(2101)], the sequence
simply "jumps" to a different point in the same
pattern, "dropping back" 12 entries [or equivalently,
"skipping ahead" 16 entries], but still continuing
with the same repeating [period 28] pattern. Every
year has at least 1 "Friday the 13th," and no year has
more than 3. On average, 3 of every 7 years (43%) have
1 "Friday the 13th," 3 of every 7 years (43%) have 2
of them, and only 1 in 7 years (14%) has 3 of them.
Conjecture: The same basic repeating pattern results
if we seek the number of "Sunday the 22nds" or
"Wednesday the 8ths" or anything else similar, with
the only difference being that the sequence starts at
a different point in the repeating pattern.
	
EXAMPLE 	

a(2004) = 2, since there were 2 "Friday the 13ths"
that year: February 13,2004 and August 13, 2004 both
fell on a Friday.

MATHEMATICA 	

(*Load <<Miscellaneous`Calendar` package first*) s={};
For[n=1901, n<=2200, t=0; For[m=1, m<=12,
If[DayOfWeek[{n, m, 13}]===Friday, t++ ]; m++ ];
AppendTo[s, t]; n++ ]; s
	
KEYWORD nonn

AUTHOR 	

Adam M. Kalman (mocha(AT)clarityconnect.com), Dec 22
2004

--- honak3r at bvunet.net
<http://us.f551.mail.yahoo.com/ym/Compose?To=honak3r@bvunet.net&YY=95130&y5beta=yes&y5beta=yes&order=down&sort=date&pos=0&view=a&head=b>
wrote:

> > It's double-13 Friday. All the
> > numbers in the numerical notation -- 10/13/2006 --
> add up
> > to 13 as well.
>
>
> Thanks for that, I appreciate it.
>
> What I'd like to know, is when is it going to occur
> again?
>
> G. L.

To: editor
Subject: New Prime Curio about 10132006 by Post
From: Prime Curios! automailer for
<jvospost2 at yahoo.com
<http://us.f551.mail.yahoo.com/ym/Compose?To=jvospost2@yahoo.com&YY=93458&y5beta=yes&y5beta=yes&order=down&sort=date&pos=0&view=a&head=b>>

There has been a new curio submitted for your
approval:

10132006 [number_id=6569]

Some people fear the prime 13, especially on Fridays.
Curiously so on 10/13/2006, whose digits concatenate
as
10132006. <a href=
"http://washingtontimes.com/national/20061012-115954-3697r.htm">
For the fearful, this Friday has their number By
Jennifer Harper THE WASHINGTON TIMES October 13,
2006</a>

This is not a good day for paraskevidekatriaphobics --
those who fear Friday the 13th. It's double-13 Friday.
All the numbers in the numerical notation --10/13/2006
-- add up to 13 as well, giving great pause to the
superstitious. The phenomenon hasn't happened in 476
years, said Heinrich Hemme, a physicist at Germany's
University of Aachen who crunched the numbers to find
that the double-whammy last occurred Jan. 13, 1520.

"Pure chance," the good professor told the press
yesterday.

But it's not exactly TGIF for the 21 million Americans
who fear the day. Some may not travel or even get out
of bed, said Donald Dossey, a North Carolina
psychologist who coined the term
"paraskevidekatriaphobia" 20 years ago. He estimates
that the nation is out $900 million in lost
productivity because of Friday the 13th sick-outs...
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20061014/359668c6/attachment-0001.htm>