MONDAY, 18 FEBRUARY 2013

Today is $49^{th}$ day of the year.

$49$ is a perfect square.

$49$ is also a lucky number.

The best description of lucky numbers that I have come across is from Ivars Peterson's MathTrak blog which I quote from below:

Hunting for prime numbers, those evenly divisible only by themselves and 1, requires a sieve to separate them from the rest. For example, the sieve of Eratosthenes, named for a Greek mathematician of the third century B.C., generates a list of prime numbers by the process of elimination.
To find all prime numbers less than, say, 100, the hunter writes down all the integers from 2 to 100 in order (1 doesn't count as a prime). First, 2 is circled, and all multiples of 2 (4, 6, 8, and so on) are struck from the list. That eliminates composite numbers that have 2 as a factor. The next unmarked number is 3. That number is circled, and all multiples of 3 are crossed out. The number 4 is already crossed out, and its multiples have also been eliminated. Five is the next unmarked integer. The procedure continues in this way until only prime numbers are left on the list. Though the sieving process is slow and tedious, it can be continued to infinity to identify every prime number.
Other types of sieves isolate different sequences of numbers. Around 1955, the mathematician Stanislaw Ulam (1909-1984) identified a particular sequence made up of what he called "lucky numbers," and mathematicians have been playing with them ever since.
Starting with a list of integers, including 1, the first step is to cross out every second number: 2, 4, 6, 8, and so on, leaving only the odd integers. The second integer not crossed out is 3. Cross out every third number not yet eliminated. This gets rid of 5, 11, 17, 23, and so on. The third surviving number from the left is 7; cross out every seventh integer not yet eliminated: 19, 39, ... Now, the fourth number from the beginning is 9. Cross out every ninth number not yet eliminated, starting with 27.
This particular sieving process yields certain numbers that permanently escape getting killed. That's why Ulam called them "lucky." See the table below for a list of lucky numbers less than 200.
1 3 7 9 13 15 21 25 31 33 37 43 49 51 63 67 69 73 75 79 87 93 99 105 111 115 127 129 133 135 141 151 159 163 169 171 189 193 195

These lucky numbers should not be confused with Euler's Lucky Numbers, see http://oeis.org/A014556.

For those that are interested, the $66$ days of this year that are related to a lucky number are:

Lucky Number	Date
1	Tuesday 1 January
3	Thursday 3 January
7	Monday 7 January
9	Wednesday 9 January
13	Sunday 13 January
15	Tuesday 15 January
21	Monday 21 January
25	Friday 25 January
31	Thursday 31 January
33	Saturday 2 February
37	Wednesday 6 February
43	Tuesday 12 February
49	Monday 18 February
51	Wednesday 20 February
63	Monday 4 March
67	Friday 8 March
69	Sunday 10 March
73	Thursday 14 March
75	Saturday 16 March
79	Wednesday 20 March
87	Thursday 28 March
93	Wednesday 3 April
99	Tuesday 9 April
105	Monday 15 April
111	Sunday 21 April
115	Thursday 25 April
127	Tuesday 7 May
129	Thursday 9 May
133	Monday 13 May
135	Wednesday 15 May
141	Tuesday 21 May
151	Friday 31 May
159	Saturday 8 June
163	Wednesday 12 June
169	Tuesday 18 June
171	Thursday 20 June
189	Monday 8 July
193	Friday 12 July
195	Sunday 14 July
201	Saturday 20 July
205	Wednesday 24 July
211	Tuesday 30 July
219	Wednesday 7 August
223	Sunday 11 August
231	Monday 19 August
235	Friday 23 August
237	Sunday 25 August
241	Thursday 29 August
259	Monday 16 September
261	Wednesday 18 September
267	Tuesday 24 September
273	Monday 30 September
283	Thursday 10 October
285	Saturday 12 October
289	Wednesday 16 October
297	Thursday 24 October
303	Wednesday 30 October
307	Sunday 3 November
319	Friday 15 November
321	Sunday 17 November
327	Saturday 23 November
331	Wednesday 27 November
339	Thursday 5 December
349	Sunday 15 December
357	Monday 23 December
361	Friday 27 December