Randy Holloway at Microsoft

Tip: search.msn.com (or any other search engine)

Or better yet, solve it without using a search engine.

-Don

Interesting way to recruit. I've been away from math way too long..wouldn't have caught the 'rational' with the functions. Found some really cool A/I sites when looking for the solution!! Aaahh, the days of Lisp and Prolog!!

Here is an expanded natural log (Leonard Euler's baby) and the answer to f(5) is in here. I have probably wasted too much time on trying to find a sequence or what the actual function is. Seems related to the 10 digit prime numbers.

2.718281828459045235360287471352662497
7572470936999595749669676277240766303535
4759457138217852516642742746639193200305
9921817413596629043572900334295260595630
7381323286279434907632338298807531952510
1901157383418793070215408914993488416750
9244761460668082264800168477411853742345
4424371075390777449920695517027618386062
6133138458300075204493382656029760673711
3200709328709127443747047230696977209310
1416928368190255151086574637721112523897
8442505695369677078544996996794686445490
5987931636889230098793127736178215424999
2295763514822082698951936680331825288693
9849646510582093923982948879332036250944
3117301238197068416140397019837679320683
2823764648042953118023287825098194558153
0175671736133206981125099618188159304169
0351598888519345807273866738589422879228
4998920868058257492796104841984443634632
4496848756023362482704197862320900216099
0235304369941849146314093431738143640546

still wasting time.. Okay, these numbers aren't prime numbers (should not have read anything first). All numbers add up to 49. coincidence? Maybe. I have a few sequences with positioning too. Some are very interesting..Don't think I have it sealed yet.

/**********
I loaded the expanded natural log into a single column table of text. Ran this script on it to get the answer.
**********/

DECLARE @TextLength INT
DECLARE @i SMALLINT
DECLARE @Sum SMALLINT
DECLARE @Fn SMALLINT
--
SELECT @TextLength = LEN(text) FROM Table1
SET @i = 1
SET @Fn = 0
--
CREATE TABLE #tempForOutput ([Function] SMALLINT,
Position SMALLINT,
Numbers CHAR(10))
--
WHILE (@i < (@TextLength - 9))
BEGIN
SELECT @Sum =CAST(SUBSTRING(Text, @i, 1) AS INT) +
CAST(SUBSTRING(Text, @i + 1, 1) AS INT) +
CAST(SUBSTRING(Text, @i + 2, 1) AS INT) +
CAST(SUBSTRING(Text, @i + 3, 1) AS INT) +
CAST(SUBSTRING(Text, @i + 4, 1) AS INT) +
CAST(SUBSTRING(Text, @i + 5, 1) AS INT) +
CAST(SUBSTRING(Text, @i + 6, 1) AS INT) +
CAST(SUBSTRING(Text, @i + 7, 1) AS INT) +
CAST(SUBSTRING(Text, @i + 8, 1) AS INT) +
CAST(SUBSTRING(Text, @i + 9, 1) AS INT)
FROM Table1
--
IF @Sum = 49
BEGIN
SET @Fn = @Fn + 1
INSERT INTO #tempForOutput
SELECT @Fn,
@i,
SUBSTRING(Text, @i, 10)
FROM Table1
END
--
SET @i = @i + 1
END
SELECT * FROM #tempForOutput
DROP TABLE #tempForOutput

/***************
Function Position Numbers
-------- -------- ----------
1 1 7182818284
2 5 8182845904
3 23 8747135266
4 99 7427466391
5 127 5966290435
6 145 2952605956
7 283 0753907774
8 288 0777449920
9 382 3069697720
10 428 1252389784
11 481 3163688923
12 515 9229576351
13 525 4822082698
14 580 8879332036
15 633 6832823764
16 634 8328237646
17 666 8194558153
18 696 2509961818

(18 row(s) affected)
****************/