Search: id:A007931
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%I A007931
%S A007931 1,2,11,12,21,22,111,112,121,122,211,212,221,222,1111,1112,1121,1122,
%T A007931 1211,1212,1221,1222,2111,2112,2121,2122,2211,2212,2221,2222,11111,
%U A007931 11112,11121,11122,11211,11212,11221,11222,12111,12112,12121,12122
%N A007931 Numbers that contain only 1's and 2's. Nonempty binary strings of length 
               n in lexicographic order.
%C A007931 Logic-binary sequence: prefix it by the empty word to have all binary 
               words on the alphabet {1,2}.
%C A007931 The least binary word of length k is a(2^k - 1).
%D A007931 K. Atanassov, On the 97-th, 98-th and the 99-th Smarandache Problems, 
               Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, 
               Vol. 5 (1999), No. 3, 89-93.
%D A007931 K. Atanassov, On Some of Smarandache's Problems, American Research Press, 
               1999, 16-21.
%D A007931 F. Smarandache, Only Problems, not Solutions!, Xiquan Publ., Phoenix-Chicago, 
               1993.
%D A007931 James E. Foster, A Number System without a Zero-Symbol, Mathematics Magazine, 
               Vol. 21, No. 1. (1947), pp. 39-41.
%H A007931 K. Atanassov, <a href="http://www.gallup.unm.edu/~smarandache/Atanassov-SomeProblems.pdf">
               On Some of Smarandache's Problems</a>
%H A007931 R. R. Forslund, <a href="http://www.emis.de/journals/SWJPAM/Vol1_1995/
               rrf01.ps">A logical alternative to the existing positional number 
               system</a>, Southwest Journal of Pure and Applied Mathematics, Vol. 
               1, 1995.
%H A007931 R. R. Forslund, <a href="http://my.tbaytel.net/~forslund/index.html">
               Positive Integer Pages</a>
%H A007931 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">
               Only Problems, Not Solutions!</a>.
%H A007931 EMIS, <a href="http://www.emis.de/journals/SWJPAM/vol1-95.html">Mirror 
               site for Southwest Journal of Pure and Applied Mathematics</a>
%F A007931 To get a(n), write n+1 in base 2, remove initial 1, add 1 to all remaining 
               digits: e.g. 11 in base 2 is 1011; remove initial 1 and add 1 to 
               remaining digits: a(10)=122. - Clark Kimberling (ck6(AT)evansville.edu), 
               Mar 11 2003
%F A007931 a(n) = A053645(n+1)+A002275(A000523(n)) = a(n-2^b(n))+10^b(n) where b(n) 
               = A059939(n) = floor[log2(n+1)-1] - Henry Bottomley (se16(AT)btinternet.com), 
               Feb 14 2001
%t A007931 f[n_] := FromDigits[Rest@IntegerDigits[n + 1, 2] + 1]; Array[f, 42] (* 
               Robert G. Wilson v Sep 14 2006 *)
%Y A007931 Cf. A007931, A059893, A007932, A045670, A052382, A059939, A059941, A059943, 
               A032924.
%Y A007931 Sequence in context: A038115 A089604 A038114 this_sequence A136407 A136999 
               A053880
%Y A007931 Adjacent sequences: A007928 A007929 A007930 this_sequence A007932 A007933 
               A007934
%K A007931 nonn,base,nice,easy
%O A007931 1,2
%A A007931 R. Muller

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