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 A067894 Write 0, 1, ..., n in binary and add as if they were decimal numbers. 7
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 9 18:23 EDT 2023. Contains 363183 sequences. (Running on oeis4.)