A162951 - OEIS

A162951

a(1)=0. a(n) is the smallest integer > a(n-1) such that both a(n) and a(n)-a(n-1) have the same number of 1's when written in binary as n has when it is written in binary.

%I #8 Mar 11 2014 01:32:43

%S 0,1,6,8,17,20,41

%N a(1)=0. a(n) is the smallest integer > a(n-1) such that both a(n) and a(n)-a(n-1) have the same number of 1's when written in binary as n has when it is written in binary.

%C a(7)=41 is the final term because 8 has one binary 1, which means that a(8), if it existed, must be a power of 2, and a(8)-41 must be a power of 2. Since no two powers of 2 have a difference of 41, then the sequence has only 7 terms.

%t nxt[{n_,a_}]:=Module[{k=a+1},While[DigitCount[n+1,2,1] != DigitCount[k,2,1] || DigitCount[k,2,1] != DigitCount[k-a,2,1],k++];{n+1,k}]; Transpose[ NestList[nxt,{1,0},6]][[2]] (* _Harvey P. Dale_, Dec 07 2012 *)

%K fini,full,nonn

%O 1,3

%A _Leroy Quet_, Jul 18 2009