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

0,3

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

See A118249 for the concatenation of the reversed binary representations.

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

Sequence in context: A344168 A239142 A028288 * A278998 A211533 A079136

Adjacent sequences: A118247 A118248 A118249 * A118251 A118252 A118253

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

Status

approved