

A225237


Numbers n such that n occurs within its base 2 representation regarded as a fixed necklace.


1



0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1100, 1101, 1111, 10000, 10001, 10011, 10100, 10101, 10111, 11000, 11001, 11100, 11101, 100000, 100001, 101000, 101010, 101100, 101101, 101111, 110000, 110001, 110101, 110110, 111011, 111100, 111101, 1000000
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

Every power of 10 occurs in this sequence.


LINKS

Table of n, a(n) for n=1..38.
Eric W. Weisstein, MathWorld: Necklace


EXAMPLE

10 (in base 10) = 1010 (in base 2). Regarding this base 2 representation as a fixed necklace, we can list characters in the order 1010 by starting with the first character. In this listing 10 occurs ({10}10). Thus 10 is in the sequence.
111011 (in base 10) = 11011000110100011 (in base 2). Regarding this base 2 representation as a fixed necklace, we can list characters in the order 11110110001101000 by starting with the characters "11" at the end of the base 2 representation. In this listing 111011 occurs (1{111011}0001101000). Thus 111011 is in the sequence.


PROG

(PARI){inseq(w)=local(bw, mm, texp, btod, bigb, lbb, swsq, ii);
bw=binary(w);
mm=length(bw); texp=0; btod=0;
forstep(i=mm, 1, 1, btod=btod+bw[i]*10^texp; texp++);
bigb=binary(btod); lbb=length(bigb);
for(k=0, lbb  1 , swsq=1;
for(j=1, mm, ii=(j+k)%lbb; if(ii==0, ii=lbb);
if(bw[j]!=bigb[ii], swsq=1));
if(swsq==1, break)
); if(swsq==1, swsq=btod);
return(swsq)}
{ptd=0; for(w=0, 10^9, jj=inseq(w); if(jj>=0, ptd++; print1(jj, ", "); if(ptd>39, break)))}


CROSSREFS

A038102 is a subsequence of this. For the terms of the sequence not found in A038102, see A225238.
Sequence in context: A136814 A136809 A136813 * A038102 A181891 A115846
Adjacent sequences: A225234 A225235 A225236 * A225238 A225239 A225240


KEYWORD

nonn,base


AUTHOR

Douglas Latimer, May 04 2013


STATUS

approved



