A067894 - OEIS

%I #29 Oct 29 2022 11:51:38

%S 0,1,11,22,122,223,333,444,1444,2445,3455,4466,5566,6667,7777,8888,

%T 18888,28889,38899,48910,59010,69111,79221,89332,100332,111333,122343,

%U 133354,144454,155555,166665,177776,277776,377777,477787,577798,677898,777999,878109

%N Write 0, 1, ..., n in binary and add as if they were decimal numbers.

%C a(n) == floor((n+1)/2) (mod 10). - _Robert G. Wilson v_, May 15 2003

%H Harvey P. Dale, <a href="/A067894/b067894.txt">Table of n, a(n) for n = 0..1000</a>

%H Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2210.10968">Identities and periodic oscillations of divide-and-conquer recurrences splitting at half</a>, arXiv:2210.10968 [cs.DS], 2022, pp. 43-44.

%e a(6) = 0 + 1 + 10 + 11 + 100 + 101 + 110 = 333.

%p for n from 0 to 50 do s := 0: for j from 0 to n do s := s+convert(j, binary): od: printf(`%d,`,s): od:

%t f[n_] := Apply[Plus, Table[ FromDigits[ IntegerDigits[i, 2]], {i, 0, n}]]; Table[ f[n], {n, 0, 36}]

%t Accumulate[Table[FromDigits[IntegerDigits[n,2]],{n,0,40}]] (* _Harvey P. Dale_, Dec 30 2015 *)

%Y Cf. A067895.

%Y Partial sums of A007088.

%K nonn,base,easy

%O 0,3

%A _N. J. A. Sloane_, based on a suggestion of Anne Donovan (anned3005(AT)aol.com) May 15 2003

%E More terms from _Robert G. Wilson v_, _Ray Chandler_ and _James A. Sellers_, May 15 2003