A179857 Smallest number greater than n having in binary representation exactly twice the number of ones as n has in binary representation.

3, 3, 15, 5, 15, 15, 63, 9, 15, 15, 63, 15, 63, 63, 255, 17, 23, 23, 63, 23, 63, 63, 255, 27, 63, 63, 255, 63, 255, 255, 1023, 33, 39, 39, 63, 39, 63, 63, 255, 43, 63, 63, 255, 63, 255, 255, 1023, 51, 63, 63, 255, 63, 255, 255, 1023, 63, 255, 255, 1023, 255, 1023, 1023

Offset: 1

Author

Reinhard Zumkeller, Jul 31 2010

Keywords

• base
• nonn

Comments

a(n) = Min{m: m > n and A000120(m) = 2*A000120(n)};

a(n) is odd;

n < a(n) < A000290(A062383(n));

a(A000079(n)) = A000051(n);

A024036 and A000225 give record values and where they occur.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000120, A086799.

Cf. A000290, A062383.

Cf. A000051, A000079.

Cf. A000225, A024036.

Programs

Mathematica

br2[n_]:=Module[{k=If[EvenQ[n],n+1,n+2],t=2*DigitCount[n,2,1]},While[ DigitCount[ k,2,1]!=t,k=k+2];k]; Array[br2,70] (* Harvey P. Dale, Sep 20 2016 *)

PARI

a(n) = my(k=n+1, h=hammingweight(n)); while (hammingweight(k) != 2*h, k++); k; \\ Michel Marcus, Nov 13 2023

Extensions

Definition clarified by Harvey P. Dale, Sep 20 2016