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

Author

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

Keywords

• nonn
• base
• easy

Comments

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

Examples

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

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.

Crossrefs

Cf. A067895.

Partial sums of A007088.

Programs

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 *)

Extensions

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