A225237 Numbers n such that n occurs within its base 2 representation regarded as a fixed necklace.
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
Offset: 1
Examples
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.
Links
- Eric W. Weisstein, MathWorld: Necklace
Crossrefs
Programs
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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)))}
Comments