1,1

Also numbers n such that the binary digital mean dm(2, n) = sigma(i in [1, d]: d_i * 2 - 1) / (2 * d) = 0, where d is the number of digits in the binary representation of n and d_i the individual digits. [From Reikku Kulon (reikku(AT)gmail.com), Sep 21 2008]

Contribution from Reikku Kulon (reikku(AT)gmail.com), Sep 29 2008: (Start)

Each run of values begins with 2^(2k + 1) + 2^(k + 1) - 2^k - 1. The initial values increase according to the sequence {2^(k - 1), 2^(k - 2), 2^(k - 3), ..., 2^(k - k)}.

After this, the values follow a periodic sequence of increases by successive powers of two with single odd values interspersed.

Each run ends with an odd increase followed by increases of {2^(k - k), ..., 2^(k - 2), 2^(k - 1), 2^k}, finally reaching 2^(2k + 2) - 2^(k + 1).

Similar behavior occurs in other bases. (End)

Numbers n such that A000120(n)/A031443(n) = 1/2. [From Ctibor O. Zizka (c.zizka(AT)email.cz), Oct 15 2008]

Reikku Kulon, Table of n, a(n) for n in [1, 10000]

a(n+1)=a(n)+2^k+2^(m-1)-1+int((2^(k+m)-2^k)/a(n))*(2^(2*m)+2^(m-1)) where k is the largest integer such that 2^k divides a(n) and m is the largest integer such that 2^m divides a(n)/2^k+1 - Ulrich Schimke (UlrSchimke(AT)aol.com)

A145037(a(n)) equals zero. [From Reikku Kulon (reikku(AT)gmail.com), Oct 02 2008]

9 is present because '1001' contains 2 '0's and 2 '1's

(Maple) a:=proc(n) local nn, n1, n0: nn:=convert(n, base, 2): n1:=add(nn[i], i=1..nops(nn)): n0:=nops(nn)-n1: if n0=n1 then n else end if end proc: seq(a(n), n= 1.. 240); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 31 2008]

f0[n_]:=DigitCount[n, 2, 0]; f1[n_]:=DigitCount[n, 2, 1]; f[n_]:=f1[n]/f0[n]; lst={}; Do[If[f[n]==1, AppendTo[lst, n]], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 21 2009]

(C) int recursive (int n) {int nWork, result, k, m; for (nWork=n, k=0; nWork%2==0; k++, nWork/=2); nWork++; for (m=0; nWork%2==0; m++, nWork/=2); result=n+pow(2, k)+pow(2, m-1)-1; result+=(int)((pow(2, k+m)-pow(2, k))/n) * (pow(2, 2*m)+pow(2, m-1)); return (result); }

(PARI) for(n=1, 100, b=binary(n); l=length(b); if(sum(i=1, l, component(b, i))==l/2, print1(n, ", ")))

Cf. A049354-A049360. See also A061854, A037861. Terms of binary width n are enumerated by A001700.

Cf. A144777, A144798, A144799, A144800, A144801, A144812 (subsets).

Cf. A000120, A001316, A006519, A145057, A145058, A145059, A145060, A144912, A145037.

Sequence in context: A135782 A037457 A037314 this_sequence A051017 A078180 A058890

Adjacent sequences: A031440 A031441 A031442 this_sequence A031444 A031445 A031446

nonn,base,easy,nice

Clark Kimberling (ck6(AT)evansville.edu)