A181891 Numbers n such that n is the substring identical to the least significant bits of its base 2 representation.

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

Offset

1,3

Comments

Terms with odd index, that is, a(1), a(3), a(5), ... are all multiples of 10. Each even-index term is one more than its predecessor, so that a(2n) = a(2n-1) + 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 two-digit 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 A352103 A066334

Adjacent sequences: A181888 A181889 A181890 * A181892 A181893 A181894

Keyword

nonn,base,easy

Author

Douglas Latimer, Mar 30 2012

Status

approved