A067894 Write 0, 1, ..., n in binary and add as if they were decimal numbers.

0, 1, 11, 22, 122, 223, 333, 444, 1444, 2445, 3455, 4466, 5566, 6667, 7777, 8888, 18888, 28889, 38899, 48910, 59010, 69111, 79221, 89332, 100332, 111333, 122343, 133354, 144454, 155555, 166665, 177776, 277776, 377777, 477787, 577798, 677898, 777999, 878109

Offset

0,3

Comments

a(n) == floor((n+1)/2) (mod 10). - Robert G. Wilson v, May 15 2003

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, pp. 43-44.

Example

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

Maple

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:

Mathematica

f[n_] := Apply[Plus, Table[ FromDigits[ IntegerDigits[i, 2]], {i, 0, n}]]; Table[ f[n], {n, 0, 36}]
Accumulate[Table[FromDigits[IntegerDigits[n, 2]], {n, 0, 40}]] (* Harvey P. Dale, Dec 30 2015 *)

Crossrefs

Cf. A067895.

Partial sums of A007088.

Sequence in context: A213972 A061852 A083511 * A094620 A077431 A118133

Adjacent sequences: A067891 A067892 A067893 * A067895 A067896 A067897

Keyword

nonn,base,easy

Author

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

Extensions

More terms from Robert G. Wilson v, Ray Chandler and James A. Sellers, May 15 2003

Status

approved