cp's OEIS Frontend

A118248 Least nonnegative integer whose binary representation does not occur in the concatenation of the binary representations of all earlier terms.

%I A118248 #44 Aug 20 2017 10:02:46
%S A118248 0,1,2,4,7,8,11,16,18,21,22,25,29,31,32,35,36,38,40,58,64,67,68,70,75,
%T A118248 76,78,87,88,90,93,99,101,104,107,122,128,131,133,134,136,138,140,144,
%U A118248 148,150,152,155,156,159,161,169,170,172,178,183,188,190
%N A118248 Least nonnegative integer whose binary representation does not occur in the concatenation of the binary representations of all earlier terms.
%C A118248 Otherwise said: Omit numbers whose binary representation already occurs in the concatenation of the binary representation of earlier terms. As such, a binary analog of A048991 / A048992 (Hannah Rollman's numbers), rather than "early bird" binary numbers A161373. - _M. F. Hasler_, Jan 03 2013
%H A118248 Rainer Rosenthal, <a href="/A118248/b118248.txt">Table of n, a(n) for n = 0..9999</a>
%H A118248 Nick Hobson, <a href="/A118248/a118248.py.txt">Python program for this sequence</a>
%t A118248 Block[{b = {{0}}, a = {0}, k, d}, Do[k = FromDigits[#, 2] &@ Last@ b + 1; While[SequenceCount[Flatten@ b, Set[d, IntegerDigits[k, 2]]] > 0, k++]; AppendTo[b, d]; AppendTo[a, k], {i, 57}]; a] (* _Michael De Vlieger_, Aug 19 2017 *)
%o A118248 (PARI) A118248(n,show=0,a=0)={my(c=[a],find(t,s,L)=L || L=#s; for(i=0,#t-L, vecextract( t,(2^L-1)<<i )==s & return(1))); for(k=1,n, show && print1(a","); while( find(c,binary(a++)),); c=concat(c,binary(a)));a}  \\ _M. F. Hasler_, Jan 03 2013
%o A118248 (Perl) $s="";$i=0;do{$i++;$b=sprintf("%b",$i);if(index($s,$b)<0){print("$i=$b\n");$s.=$b}}while(1);
%Y A118248 Cf. A118247 (concatenation of binary representations), A118250, A118252 (variants where binary representations are reversed).
%K A118248 easy,nonn
%O A118248 0,3
%A A118248 _Leroy Quet_, Apr 18 2006
%E A118248 More terms from _Graeme McRae_, Apr 19 2006
%E A118248 Explicit definition from _M. F. Hasler_, Dec 29 2012
%E A118248 Perl program by _Phil Carmody_, Mar 19 2015
%E A118248 Crossref and Perl program by _Phil Carmody_, Mar 19 2015