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

Author

Douglas Latimer, Mar 30 2012

Keywords

• nonn
• base
• easy

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]

Examples

			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.
		

Links

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

Crossrefs

This is a subsequence of A038102. Sequence A181929 has similar definition.

Programs

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 *)

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)))}