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.

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

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..7.

Mathematica

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 *)

Crossrefs

Sequence in context: A127400 A315941 A025081 * A032411 A345034 A058098

Adjacent sequences: A162948 A162949 A162950 * A162952 A162953 A162954

Keyword

fini,full,nonn

Author

Leroy Quet, Jul 18 2009

Status

approved