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A225238 Numbers n such that n occurs within its base 2 representation regarded as a fixed necklace, but n is not a substring of the base 2 representation regarded as a string. 1
1111, 110110, 111011, 1011110, 1101111, 10011001, 10100110, 11001010, 11010011, 110011111, 111010011, 111011101, 1001101111, 11001101111, 11010010100, 100101110100, 101000111011, 101011001010, 101111110111, 110011001100, 110111001101, 111011110011 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

No power of 10 can occur in this sequence.

LINKS

Table of n, a(n) for n=1..22.

Eric W. Weisstein, MathWorld: Necklace

EXAMPLE

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). 111011 however does not occur in the original base 2 representation 11011000110100011. Thus 111011 is in the sequence.

PROG

(PARI) {inseq(w)=local(bw, mm, texp, btod, bigb, lbb, swsq, ii, hwf);

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, hwf=k; break));

if(swsq==1, if(hwf>lbb-mm, swsq=btod, swsq=-1)); return(swsq)}

{ptd=0; for(w=0, 10^9, jj=inseq(w); if(jj>=0, ptd++; print1(jj, ", "); if(ptd>23, break)))}

CROSSREFS

The union of A038102 and this sequence is A225237.

Sequence in context: A115781 A115802 A115812 * A275944 A291945 A015292

Adjacent sequences:  A225235 A225236 A225237 * A225239 A225240 A225241

KEYWORD

nonn,base

AUTHOR

Douglas Latimer, May 04 2013

STATUS

approved

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Last modified October 17 14:56 EDT 2018. Contains 316282 sequences. (Running on oeis4.)