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

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, 76, 78, 87, 88, 90, 93, 99, 101, 104, 107, 122, 128, 131, 133, 134, 136, 138, 140, 144, 148, 150, 152, 155, 156, 159, 161, 169, 170, 172, 178, 183, 188, 190

Offset: 0

Author

Leroy Quet, Apr 18 2006

Keywords

• easy
• nonn

Comments

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

Links

• Rainer Rosenthal, Table of n, a(n) for n = 0..9999
• Nick Hobson, Python program for this sequence

Crossrefs

Cf. A118247 (concatenation of binary representations), A118250, A118252 (variants where binary representations are reversed).

Programs

Mathematica

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 *)

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)<M. F. Hasler, Jan 03 2013

Perl

$s="";$i=0;do{$i++;$b=sprintf("%b",$i);if(index($s,$b)<0){print("$i=$b\n");$s.=$b}}while(1);

Extensions

More terms from Graeme McRae, Apr 19 2006

Explicit definition from M. F. Hasler, Dec 29 2012

Perl program by Phil Carmody, Mar 19 2015

Crossref and Perl program by Phil Carmody, Mar 19 2015