A067895 -id:A067895 - cp's OEIS frontend

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

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

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

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

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.

Cf. A067895.

Partial sums of A007088.

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:

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 *)

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

A122613 Integers 1 through n written in primorial base, summed as if decimal.

Original entry on oeis.org

1, 11, 22, 42, 163, 264, 374, 485, 605, 726, 926, 1127, 1337, 1548, 1768, 1989, 2289, 2590, 2900, 3211, 3531, 3852, 4252, 4653, 5063, 5474, 5894, 6315, 7315, 8316, 9326, 10337, 11357, 12378, 13478, 14579, 15689, 16800, 17920, 19041, 20241, 21442

Offset: 1

Jonathan Vos Post, Sep 20 2006

cf. A049345 n written in primorial base [Places reading from right have values (1, 2, 6, 30, 210, ...) = primorials]. Primes in this sequence are a(2) = 11, a(6) = 163, a(33) = 10337.

			a(1) = A049345(1) = 1.
a(2) = A049345(1) + A049345(2) = 1 + 10 = 11.
a(3) = A049345(1) + A049345(2) + A049345(3) = 1 + 10 + 11 = 22.
a(4) = 1 + 10 + 11 + 20 = 42.
a(5) = 1 + 10 + 11 + 20 + 21 = 63.
a(6) = 1 + 10 + 11 + 20 + 21 + 100 = 163.
a(33) = 1 + 10 + 11 + 20 + 21 + 100 + 101 + 110 + 111 + 120 + 121 + 200 + 201 + 210 + 211 + 220 + 221 + 300 + 301 + 310 + 311 + 320 + 321 + 400 + 401 + 410 + 411 + 420 + 421 + 1000 + 1001 + 1010 + 1011 = 10337.

Cf. Primorials: A002110, factorial base A007623, A000040, A001358, A007088, A004676, A020767, A038506, A067894, A067895, A121718, A122466, A122467.

cp's OEIS Frontend

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

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