A135569 a(n) = S2(n)*2^n; where S2(n) is digit sum of n, n in binary notation.

0, 2, 4, 16, 16, 64, 128, 384, 256, 1024, 2048, 6144, 8192, 24576, 49152, 131072, 65536, 262144, 524288, 1572864, 2097152, 6291456, 12582912, 33554432, 33554432, 100663296, 201326592, 536870912, 805306368, 2147483648, 4294967296

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

For all n we have 2/n <= a(n+1)/a(n)<= 4. This holds because a(2^n -1)= n*2^(2^n -1); a(2^n) = 2^2^n; a(2^n +1) = 4*2^2^n.

a(n) = A000120(n)*2^n. - R. J. Mathar, Mar 03 2008

Maple

A000120 := proc(n) add(i, i=convert(n, base, 2)) ; end: A135569 := proc(n) A000120(n)*2^n ; end: seq(A135569(n), n=0..80) ; # R. J. Mathar, Mar 03 2008

Mathematica

Table[DigitCount[n, 2, 1]*2^n, {n, 0, 25}] (* G. C. Greubel, Oct 19 2016 *)

Crossrefs

Cf. A000120, A010060.

Sequence in context: A067846 A155893 A196202 * A370874 A337109 A210579

Adjacent sequences: A135566 A135567 A135568 * A135570 A135571 A135572

Keyword

easy,nonn,base

Author

Ctibor O. Zizka, Feb 23 2008, Mar 03 2008

Extensions

Corrected and extended by R. J. Mathar, Mar 03 2008

Status

approved