Lucky number

In Mathematical, a lucky number is a natural Nombre in a unit which is generated by a “screen” similar to the Crible of Ératosthène which generates the prime numbers. We begin with a list of whole S starting with 1:

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26, Then we remove a number on two (the second of the pair), which leaves only the odd entireties :

1,3,5,7,9,11,13,15,17,19,21,23,25, The second term of the continuation is 3. Now, we remove a number on three (the third of the first unit) among those which remain in the list:

1,3,7,9,13,15,19,21,25, The third number surviving is now 7, now, we remove a number on seven (the seventh of the first unit):

1,3,7,9,13,15,21,25, If we repeat this procedure indefinitely, the survivors are the lucky numbers:

1,3,7,9,13,15,21,25,31,33,37,43,49,51,63,67,69,73,75,79,87,93,99,…

Stanislaw Marcin Ulam was the first studied these numbers, in the neighborhoods of 1955. It named them “lucky” because of a relationship with a history called by the historian Josephus.

The lucky numbers share certain properties with the prime numbers, such as the asymptotic behavior in agreement with the Théorème of the prime numbers; the Conjecture of Goldbach was extended to them. There exists an infinity of lucky numbers. One is unaware of if there exists also an infinity of prime numbers lucky :

3,7,13,31,37,43,67,73,79,127,151,163,193,…

External bonds

Peterson, Ivars: MathTrek: Martin Gardner' S Lucky Number : http://www.sciencenews.org/sn_arc97/9_6_97/mathland.htm
Schneider, Walter: has list off the first 1000 lucky numbers : http://www.wschnei.de/number-theory/lucky-numbers-list.html
Sloane, Neil J.A.: has sequence off lucky numbers - A000959 : http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=000959
Sloane, Neil J.A.: has sequence off lucky premiums - A031157 : http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=031157
Sloane, Neil J.A.: has sequence off composite lucky numbers - A031879 : http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=031879
Weisstein, Eric W.: Lucky Number : http://mathworld.wolfram.com/LuckyNumber.html

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