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a(n) = 1 + Sum_{i=1..n} S2(i)*2^i, where S2(n) is digit sum of n, n in binary notation.
1

%I #16 Oct 24 2019 21:19:40

%S 1,3,7,23,39,103,231,615,871,1895,3943,10087,18279,42855,92007,223079,

%T 288615,550759,1075047,2647911,4745063,11036519,23619431,57173863,

%U 90728295,191391591,392718183,929589095,1734895463,3882379111

%N a(n) = 1 + Sum_{i=1..n} S2(i)*2^i, where S2(n) is digit sum of n, n in binary notation.

%H G. C. Greubel, <a href="/A135570/b135570.txt">Table of n, a(n) for n = 0..1000</a>

%t Table[1 + Sum[DigitCount[i, 2, 1]*2^i, {i, 1, n}], {n, 0, 25}] (* _G. C. Greubel_, Oct 19 2016 *)

%Y Cf. A000120, A010060.

%K easy,nonn,base

%O 0,2

%A _Ctibor O. Zizka_, Feb 23 2008, corrected Mar 03 2008

%E Offset corrected by _Alois P. Heinz_, Oct 24 2019