%I A121802
%S A121802 1,1,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0,
%T A121802 1,1,1,0,1,0,0,1
%N A121802 The numbers A121263(n) converge 2-adically. This sequence shows their 
               2-adic limit.
%C A121802 A121263 converges k-adically for any k which is not divisible by a prime 
               greater than 7.
%D A121802 David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons, 
               Problem 11286, Amer. Math. Monthly, 116 (2009) 466-467.
%D A121802 David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons 
               and Iterated Base-Changing, in "The Mathematics of Preference, Choice 
               and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, 
               William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 393-402.
%H A121802 David Applegate, Marc LeBrun and N. J. A. Sloane, <a href="http://arXiv.org/
               abs/math.NT/0611293">Descending Dungeons and Iterated Base-Changing</
               a> (arXiv:math.NT/0611293).
%e A121802 The 2-adic expansions (that is, the binary expansions written backwards) 
               of terms 30 through 43 of A121263 are:
%e A121802 30, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1]
%e A121802 31, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1]
%e A121802 32, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1]
%e A121802 33, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1]
%e A121802 34, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1]
%e A121802 35, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 
               0, 1]
%e A121802 36, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 
               0, 1, 1]
%e A121802 37, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 
               1, 0, 1, 0, 1]
%e A121802 38, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 
               0, 1, 0, 0, 0, 0, 1]
%e A121802 39, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 
               1, 0, 1, 1, 0, 0, 1, 1]
%e A121802 40, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 
               1, 0, 1, 1, 1, 1, 1, 0, 0, 1]
%e A121802 41, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 
               1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1]
%e A121802 42, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 
               0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1]
%e A121802 43, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 
               1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1]
%e A121802 44, [1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 
               0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1]
%e A121802 and we can see that the initial terms are converging.
%Y A121802 Sequence in context: A103368 A055132 A128408 this_sequence A156241 A156254 
               A010056
%Y A121802 Adjacent sequences: A121799 A121800 A121801 this_sequence A121803 A121804 
               A121805
%K A121802 nonn,more
%O A121802 0,1
%A A121802 N. J. A. Sloane (njas(AT)research.att.com), Oct 08 2006