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

0,3

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A030773 A182245 A182246 * A132679 A216576 A116617

Adjacent sequences: A118245 A118246 A118247 * A118249 A118250 A118251

Keyword

easy,nonn

Author

Leroy Quet, Apr 18 2006

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

Status

approved