A118250 The least nonnegative integer whose reversed binary representation does not occur in the concatenation of the reversed binary representations of all preceding terms.

0, 1, 3, 4, 5, 8, 10, 13, 15, 16, 18, 23, 24, 32, 35, 36, 38, 43, 55, 64, 66, 68, 70, 75, 76, 79, 83, 85, 88, 91, 95, 97, 116, 119, 120, 127, 128, 130, 132, 136, 140, 143, 147, 149, 150, 155, 157, 158, 163, 169, 170, 175, 176, 182, 186, 192, 196, 208

Offset: 0

Author

Leroy Quet, Apr 18 2006

Keywords

• easy
• nonn

Comments

"Reversed" means here "read from right to left", or "least significant bit first" (and not e.g. bitwise negation). One could also drop "reversed" everywhere and concatenate the preceding terms in decreasing order. The definition yields necessarily a strictly increasing sequence. - M. F. Hasler, Dec 29 2012

Examples

			The concatenation of the reversed binary representation of the first 5 terms (0, 1, 3, 4, 5) is concat(0,1,11,001,101)=0111001101. The reversed binary representation of the yet unused numbers 2,6,7,8,... are 01,011,111,0001,... It is seen that only the last of these four strings is not yet a substring in the above, therefore a(5)=8.
		

Links

• Rainer Rosenthal, Table of n, a(n) for n = 0..9999

Crossrefs

See A118249 for the concatenation of the reversed binary representations.

Cf. A118248 (variant without reversal), A118252 (the same with positive terms).

Programs

Mathematica

a = {{0}}; Do[k = 1; While[SequenceCount[Flatten@ a, Set[m, Reverse@ IntegerDigits[k, 2]]] > 0, k++]; AppendTo[a, m], {i, 57}]; Map[FromDigits[#, 2] &@ Reverse@ # &, a] (* Michael De Vlieger, Sep 19 2017 *)

PARI

A118250(n,show=0,a=0)={my(c=[a],S=[],L); for(k=1,n, show && print1(a","); while( setsearch(S,binary(a++)),); c=concat(binary(a),c); S=[]; for(i=0,#c-L=#binary(a), c[i+1] & for(j=i+L,min(i+L+1,#c), S=setunion(S,Set(t=[vecextract(c,2^j-2^i)])))));a}  \\ M. F. Hasler, Dec 29 2012

Extensions

More terms from Graeme McRae, Apr 19 2006

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