

A181891


Numbers n such that n is the substring identical to the least significant bits of its base 2 representation.


2



0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1100, 1101, 10000, 10001, 10100, 10101, 11000, 11001, 11100, 11101, 100000, 100001, 101100, 101101, 110000, 110001, 111100, 111101, 1000000, 1000001, 1010000, 1010001, 1100000, 1100001, 1110000, 1110001
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OFFSET

1,3


COMMENTS

Terms with odd index, that is, a(1), a(3), a(5), ... are all multiples of 10. Each evenindex term is one more than its predecessor, so that a(2n) = a(2n1) + 1. [Douglas Latimer, Apr 26 2013]


LINKS

Douglas Latimer, Table of n, a(n) for n = 1..850


EXAMPLE

The number 11 is represented in the binary system by the string "1011". 11 is a twodigit number, so we consider the 2 least significant bits, which are "11", identical to the string of digits used to represent the number 11. Thus 11 is in the sequence.


MATHEMATICA

fQ[n_] := Module[{d = IntegerDigits[n], len}, len = Length[d]; d == Take[IntegerDigits[n, 2], len]]; Select[Range[0, 1000000], fQ] (* T. D. Noe, Apr 03 2012 *)


PROG

(PARI) {for(vv=0, 200, bvv=binary(vv);
ll=length(bvv); texp=0; btod=0;
forstep(i=ll, 1, 1, btod=btod+bvv[i]*10^texp; texp++);
bigb=binary(btod); lbb=length(bigb); swsq=1;
forstep(j=ll, 1, 1, if(bvv[j]!=bigb[lbb], swsq=0); lbb);
if(swsq==1, print(btod)))}


CROSSREFS

This is a subsequence of A038102. Sequence A181929 has similar definition.
Sequence in context: A136813 A225237 A038102 * A115846 A066334 A136829
Adjacent sequences: A181888 A181889 A181890 * A181892 A181893 A181894


KEYWORD

nonn,base,easy


AUTHOR

Douglas Latimer, Mar 30 2012


STATUS

approved



