A053829 -id:A053829 - cp's OEIS frontend

A245355 Sum of digits of n written in fractional base 8/5.

0, 1, 2, 3, 4, 5, 6, 7, 5, 6, 7, 8, 9, 10, 11, 12, 7, 8, 9, 10, 11, 12, 13, 14, 12, 13, 14, 15, 16, 17, 18, 19, 11, 12, 13, 14, 15, 16, 17, 18, 13, 14, 15, 16, 17, 18, 19, 20, 18, 19, 20, 21, 22, 23, 24, 25, 14, 15, 16, 17, 18, 19, 20, 21, 13, 14, 15, 16, 17

Offset: 0

Tom Edgar, Jul 18 2014

The base 8/5 expansion is unique and thus the sum of digits function is well-defined.

			In base 8/5 the number 20 is represented by 524 and so a(20) = 5 + 2 + 4 = 11.

Amiram Eldar, Table of n, a(n) for n = 0..10000
Index entries for sequences related to fractional bases.

Cf. A000120, A007953, A024647, A053829, A244040.

a[n_] := a[n] = If[n == 0, 0, a[5 * Floor[n/8]] + Mod[n, 8]]; Array[a, 100, 0] (* Amiram Eldar, Aug 02 2025 *)

a(n) = if(n == 0, 0, a(n\8 * 5) + n % 8); \\ Amiram Eldar, Aug 02 2025

def basepqsum(p, q, n):
    L = [n]
    i = 1
    while L[i-1]>=p:
        x=L[i-1]
        L[i-1]=x.mod(p)
        L.append(q*(x//p))
        i+=1
    return sum(L)
[basepqsum(8,5,i) for i in [0..100]]

a(n) = A007953(A024647(n)).

A010070 Base 8 self or Colombian numbers (not of form k + sum of base 8 digits of k).

Original entry on oeis.org

1, 3, 5, 7, 16, 25, 34, 43, 52, 61, 70, 72, 81, 90, 99, 108, 117, 126, 135, 137, 146, 155, 164, 173, 182, 191, 200, 202, 211, 220, 229, 238, 247, 256, 265, 267, 276, 285, 294, 303, 312, 321, 330, 332, 341, 350, 359, 368, 377, 386, 395, 397, 406, 415, 424, 433

Offset: 1

Leonid Broukhis

Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.24, pp. 179-180.
József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384-386.

Cf. A003052, A010061, A010064, A010067, A053829.

s[n_] := n + Plus @@ IntegerDigits[n, 8]; m = 500; Complement[Range[m], Array[s, m]] (* Amiram Eldar, Nov 28 2020 *)

More terms from Amiram Eldar, Nov 28 2020

A053831 Sum of digits of n written in base 11.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 7, 8, 9, 10, 11, 12, 13, 14, 15

Offset: 0

Henry Bottomley, Mar 28 2000

Also the fixed point of the morphism 0->{0,1,2,3,4,5,6,7,8,9,10}, 1->{1,2,3,4,5,6,7,8,9,10,11}, 2->{2,3,4,5,6,7,8,9,10,11,12}, etc. - Robert G. Wilson v, Jul 27 2006

			a(20) = 1 + 9 = 10 because 20 is written as 19 base 11.

Tanar Ulric, Table of n, a(n) for n = 0..10000
Jeffrey O. Shallit, Problem 6450, Advanced Problems, The American Mathematical Monthly, Vol. 91, No. 1 (1984), pp. 59-60; Two series, solution to Problem 6450, ibid., Vol. 92, No. 7 (1985), pp. 513-514.
Robert Walker, Self Similar Sloth Canon Number Sequences.
Eric Weisstein's World of Mathematics, Digit Sum.

Cf. A007953, A064458, A138530.

Sum of digits of n written in bases 2-16: A000120, A053735, A053737, A053824, A053827, A053828, A053829, A053830, A007953, this sequence, A053832, A053833, A053834, A053835, A053836.

int Base11DigitSum(int n) {
   int count = 0;
   while (n != 0) { count += n % 11; n = n / 11; }
   return count;
} // Tanar Ulric, Oct 20 2021

Table[Plus @@ IntegerDigits[n, 11], {n, 0, 86}] (* or *)
Nest[ Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 10}]] &, {0}, 2] (* Robert G. Wilson v, Jul 27 2006 *)

a(n)=if(n<1,0,if(n%11,a(n-1)+1,a(n/11)))

a(n)=sumdigits(n,11) \\ Charles R Greathouse IV, Oct 20 2021

From Benoit Cloitre, Dec 19 2002: (Start)
a(0)=0, a(11n+i) = a(n)+i for 0 <= i <= 10.
a(n) = n-(m-1)*(Sum_{k>0} floor(n/m^k)) = n-(m-1)*A064458(n). (End)
a(n) = A138530(n,11) for n > 10. - Reinhard Zumkeller, Mar 26 2008
Sum_{n>=1} a(n)/(n*(n+1)) = 11*log(11)/10 (Shallit, 1984). - Amiram Eldar, Jun 03 2021

A173525 a(n) = 1 + A053824(n-1), where A053824 = sum of digits in base 5.

Original entry on oeis.org

1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 7, 8, 9, 10, 11, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 7, 8, 9, 10, 11, 8, 9, 10, 11, 12

Offset: 1

Omar E. Pol, Feb 20 2010

Also: a(n) = A053824(5^k+n-1) in the limit k->infinity, where k plays the role of a row index in A053824. (See the comment by M. F. Hasler for the proof.)
This means: if A053824 is regarded as a triangle then the rows converge to this sequence.
See conjecture in the entry A000120, and the case of base 2 in A063787.
From R. J. Mathar, Dec 09 2010: (Start)
In base b=5, A053824 starts counting up from 1 each time the index wraps around a power of b: A053824(b^k)=1.
Obvious recurrences are A053824(m*b^k+i) = m+A053824(i), 1 <= m < b-1, 0 <= i < b^(k-1).
So A053824 can be decomposed into a triangle T(k,n) = A053824(b^k+n-1), assuming that column indices start at n=1; row lengths are (b-1)*b^k.
There is a self-similarity in these sequences; a sawtooth structure of periodicity b is added algebraically on top of a sawtooth structure of periodicity b^2, on top of a periodicity b^3 etc. This leads to some "fake" finitely periodic substructures in the early parts of each row of T(.,.): often, but not always, a(n+b)=1+a(n). Often, but not always, a(n+b^2)=1+a(n) etc.
The common part of the rows T(.,.) grows with the power of b as shown in the recurrence above, and defines a(n) in the limit of large row indices k. (End)
The two definitions agree because the first 5^r terms in each row correspond to numbers 5^r, 5^r+1,...,5^r+(5^r-1), which are written in base 5 as a leading 1 plus the digits of 0,...,5^r-1. - M. F. Hasler, Dec 09 2010
From Omar E. Pol, Dec 10 2010: (Start)
In the scatter plots of these sequences, the basic structure is an element with b^2 points, where b is the associated base. (Scatter plots are created with the "graph" button of a sequence.) Sketches of these structures look as follows, the horizontal axis a squeezed version of the index n, b consecutive points packed vertically, and the vertical axis a(n):
........................................................
................................................ * .....
............................................... ** .....
..................................... * ...... *** .....
.................................... ** ..... **** .....
.......................... * ...... *** .... ***** .....
......................... ** ..... **** ... ****** .....
............... * ...... *** .... ***** ... ***** ......
.............. ** ..... **** .... **** .... **** .......
.... * ...... *** ..... *** ..... *** ..... *** ........
... ** ...... ** ...... ** ...... ** ...... ** .........
... * ....... * ....... * ....... * ....... * ..........
........................................................
... b=2 ..... b=3 ..... b=4 ..... b=5 ..... b=6 ........
. A000120 . A053735 . A053737 . A053824 . A053827 ......
. A063787 . A173523 . A173524 . A173525 . A173526 ......
........................................................
............................................. * ........
............................................ ** ........
........................... * ............. *** ........
.......................... ** ............ **** ........
........... *............ *** ........... ***** ........
.......... ** .......... **** .......... ****** ........
......... ***.......... ***** ......... ******* ........
........ **** ........ ****** ........ ******** ........
....... ***** ....... ******* ....... ********* ........
...... ****** ...... ******** ....... ******** .........
..... ******* ...... ******* ........ ******* ..........
..... ****** ....... ****** ......... ****** ...........
..... ***** ........ ***** .......... ***** ............
..... **** ......... **** ........... **** .............
..... *** .......... *** ............ *** ..............
..... ** ........... ** ............. ** ...............
..... * ............ * .............. * ................
........................................................
..... b=7 .......... b=8 ............ b=9 ..............
... A053828 ...... A053829 ........ A053830 ............
... A173527 ...... A173528 ........ A173529 ............(End)

Reinhard Zumkeller, Table of n, a(n) for n = 1..3126=5^5+1
Robert Walker, Self Similar Sloth Canon Number Sequences

Cf. A000120, A053824, A063787, A173523, A173524, A173526, A173527, A173528, A173529.

a173525 = (+ 1) . a053824 . (subtract 1) -- Reinhard Zumkeller, Jan 31 2014

A053825 := proc(n) add(d, d=convert(n,base,5)) ; end proc:
A173525 := proc(n) local b,k; b := 5 ; if n < b then n; else k := n/(b-1);   k := ceil(log(k)/log(b)) ; A053825(b^k+n-1) ; end if; end proc:
seq(A173525(n),n=1..100) ;

Total[IntegerDigits[#,5]]+1&/@Range[0,100] (* Harvey P. Dale, Jun 14 2015 *)

A173525(n)={ my(s=1); n--; until(!n\=5, s+=n%5); s } \\ M. F. Hasler, Dec 09 2010

A173525(n)={ my(s=1+(n=divrem(n-1,5))[2]); while((n=divrem(n[1],5))[1],s+=n[2]); s+n[2] } \\ M. F. Hasler, Dec 09 2010

a(n) = A053824(5^k + n - 1) where k >= ceiling(log_5(n/4)). - R. J. Mathar, Dec 09 2010

More terms from Vincenzo Librandi, Aug 02 2010

A173528 a(n) = 1 + sum of digits of n-1 written in base 8.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 2, 3, 4, 5, 6, 7, 8, 9, 3, 4, 5, 6, 7, 8, 9, 10, 4, 5, 6, 7, 8, 9, 10, 11, 5, 6, 7, 8, 9, 10, 11, 12, 6, 7, 8, 9, 10, 11, 12, 13, 7, 8, 9, 10, 11, 12, 13, 14, 8, 9, 10, 11, 12, 13, 14, 15, 2, 3, 4, 5, 6, 7, 8, 9, 3, 4, 5, 6, 7, 8, 9, 10, 4, 5, 6, 7, 8, 9, 10, 11

Offset: 1

Omar E. Pol, Feb 20 2010

If A053829 is written as a triangle then the rows converge to this sequence; see the conjecture in A000120.

The sequence is the base b=8 case in a family of 8 sequences for base b=2 (A063787) and bases 3 to 9 (A173523 to A173529). Common aspects (recurrences etc.) of these are documented in A173525.

Robert Walker, Self Similar Sloth Canon Number Sequences

Cf. A000120, A053829, A063787, A173523 - A173529.

a053829:=func< n | &+Intseq(n, 8) >; a173528:=func< n | a053829(n-1)+1 >; [ a173528(n): n in [1..90] ]; // Klaus Brockhaus, Dec 07 2010

A173528 = lambda n: 1+sum((n-1).digits(base=8)) # D. S. McNeil, Dec 07 2010

a(n) = A053829(n-1)+1.

More terms from Vincenzo Librandi, Feb 21 2010

Definition and formula added by M. F. Hasler, Dec 06 2010

A054897 a(n) = Sum_{k>0} floor(n/8^k).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12

Offset: 0

Henry Bottomley, May 23 2000

nonn

Different from the highest power of 8 dividing n!, A090617.

			a(100) = 13.
a(10^3) = 141.
a(10^4) = 1427.
a(10^5) = 14284.
a(10^6) = 142855.
a(10^7) = 1428569.
a(10^8) = 14285710.
a(10^9) = 142857138.

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Cf. A011371 and A054861 for analogs involving powers of 2 and 3.

Cf. A054899, A067080, A098844, A132032.

m:=8;
function a(n) // a = A054897
  if n eq 0 then return n;
  else return a(Floor(n/m)) + Floor(n/m);
  end if;
end function;
[a(n): n in [0..103]]; // G. C. Greubel, Apr 28 2023

Table[t=0; p=8; While[s=Floor[n/p]; t=t+s; s>0, p *= 8]; t, {n,0,100}]

def A054897(n): return (n-sum(int(d) for d in oct(n)[2:]))//7 # Chai Wah Wu, Jul 09 2022

m=8 # a = A054897
def a(n): return 0 if (n==0) else a(n//m) + (n//m)
[a(n) for n in range(104)] # G. C. Greubel, Apr 28 2023

a(n) = floor(n/8) + floor(n/64) + floor(n/512) + floor(n/4096) + ....
a(n) = (n - A053829(n))/7.
From Hieronymus Fischer, Aug 14 2007: (Start)
Recurrence:
a(n) = floor(n/8) + a(floor(n/8));
a(8*n) = n + a(n);
a(n*8^m) = n*(8^m-1)/7 + a(n).
a(k*8^m) = k*(8^m-1)/7, for 0 <= k < 8, m >= 0.
Asymptotic behavior:
a(n) = n/7 + O(log(n)),
a(n+1) - a(n) = O(log(n)); this follows from the inequalities below.
a(n) <= (n-1)/7; equality holds for powers of 8.
a(n) >= (n-7)/7 - floor(log_8(n)); equality holds for n=8^m-1, m>0.
lim inf (n/7 - a(n)) = 1/7, for n -> oo.
lim sup (n/7 - log_8(n) - a(n)) = 0, for n -> oo.
lim sup (a(n+1) - a(n) - log_8(n)) = 0, for n -> oo.
G.f.: g(x) = ( Sum_{k>0} x^(8^k)/(1-x^(8^k)) )/(1-x). (End)
Partial sums of A244413. - R. J. Mathar, Jul 08 2021

Examples added by Hieronymus Fischer, Jun 06 2012

A216789 Table read by antidiagonals: T(n,k) is the digital sum of k in base n displayed in decimal.

Original entry on oeis.org

0, 0, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 2, 1, 1, 0, 1, 2, 3, 2, 2, 0, 1, 2, 3, 1, 3, 2, 0, 1, 2, 3, 4, 2, 2, 3, 0, 1, 2, 3, 4, 1, 3, 3, 1, 0, 1, 2, 3, 4, 5, 2, 4, 4, 2, 0, 1, 2, 3, 4, 5, 1, 3, 2, 1, 2, 0, 1, 2, 3, 4, 5, 6, 2, 4, 3, 2, 3

Offset: 2

Henry Bottomley & Robert G. Wilson v, Sep 16 2012

T(n,k) is the least number of powers of n that add up to k. - Mohammed Yaseen, Nov 12 2022

			A000120   0, 1, 1, 2, 1, 2, 2, 3, 1, 2,  2,  3,  2,  3,  3,  4, 1, 2, 2
A053735   0, 1, 2, 1, 2, 3, 2, 3, 4, 1,  2,  3,  2,  3,  4,  3, 4, 5, 2
A053737   0, 1, 2, 3, 1, 2, 3, 4, 2, 3,  4,  5,  3,  4,  5,  6, 1, 2, 3
A053824   0, 1, 2, 3, 4, 1, 2, 3, 4, 5,  2,  3,  4,  5,  6,  3, 4, 5, 6
A053827   0, 1, 2, 3, 4, 5, 1, 2, 3, 4,  5,  6,  2,  3,  4,  5, 6, 7, 3
A053828   0, 1, 2, 3, 4, 5, 6, 1, 2, 3,  4,  5,  6,  7,  2,  3, 4, 5, 6
A053829   0, 1, 2, 3, 4, 5, 6, 7, 1, 2,  3,  4,  5,  6,  7,  8, 2, 3, 4
A053830   0, 1, 2, 3, 4, 5, 6, 7, 8, 1,  2,  3,  4,  5,  6,  7, 8, 9, 2
A007953   0, 1, 2, 3, 4, 5, 6, 7, 8, 9,  1,  2,  3,  4,  5,  6, 7, 8, 9
A053831   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,  1,  2,  3,  4,  5, 6, 7, 8
A053832   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,  1,  2,  3,  4, 5, 6, 7
A053833   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,  1,  2,  3, 4, 5, 6
A053834   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,  1,  2, 3, 4, 5
A053835   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,  1, 2, 3, 4
A053836   0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 2, 3

Robert Israel, Table of n, a(n) for n = 2..10012 (indices corrected to start at 2 by Sidney Cadot, Jan 07 2023)
K. Atanassov, On Some of Smarandache's Problems
Eric Weisstein's World of Mathematics, Digit Sum
Wikipedia, Digit sum

Cf. A000120, A053735, A053737, A053824, A053827, A053828, A053829, A053830, A007953, A053831, A053832, A053833, A053834, A053835, A053836.

[seq(seq(convert(convert(n-b,base,b),`+`),b=n..2,-1),n=1..15)]; # Robert Israel, Aug 02 2020

DigitSum[n_, b_: 10] := Total[IntegerDigits[n, b]]; Table[ DigitSum[n - b, b], {n, 2, 13}, {b, n, 2, -1}] // Flatten

Name and offset corrected by Mohammed Yaseen, Nov 12 2022

A309959 Product of digits of (n written in base 8).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 2, 4, 6, 8, 10, 12, 14, 0, 3, 6, 9, 12, 15, 18, 21, 0, 4, 8, 12, 16, 20, 24, 28, 0, 5, 10, 15, 20, 25, 30, 35, 0, 6, 12, 18, 24, 30, 36, 42, 0, 7, 14, 21, 28, 35, 42, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 0, 2, 4, 6, 8, 10, 12, 14, 0, 3, 6, 9, 12, 15, 18, 21, 0, 4, 8, 12, 16

Offset: 0

Ilya Gutkovskiy, Aug 24 2019

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Product of digits of (n written in base k): A309953 (k = 3), A309954 (k = 4), A309956 (k = 5), A309957 (k = 6), A309958 (k = 7), this sequence (k = 8), A309788 (k = 9), A007954 (k = 10).

Cf. A007094, A053829.

[0] cat [&*Intseq(n,8):n in [1..100]]; // Marius A. Burtea, Aug 25 2019

Table[Times @@ IntegerDigits[n, 8], {n, 0, 100}]

G.f. A(x) satisfies: A(x) = x * (1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6) * (1 + A(x^8)).

A346731 Replace 8^k with (-1)^k in base-8 expansion of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, -1, 0, 1, 2, 3, 4, 5, 6, -2, -1, 0, 1, 2, 3, 4, 5, -3, -2, -1, 0, 1, 2, 3, 4, -4, -3, -2, -1, 0, 1, 2, 3, -5, -4, -3, -2, -1, 0, 1, 2, -6, -5, -4, -3, -2, -1, 0, 1, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, -1, 0, 1, 2, 3, 4, 5, 6, -2, -1, 0, 1, 2, 3, 4, 5, -3, -2, -1, 0, 1, 2, 3, 4, -4

Offset: 0

Ilya Gutkovskiy, Jul 30 2021

If n has base-8 expansion abc..xyz with least significant digit z, a(n) = z - y + x - w + ...

			79 = 117_8, 7 - 1 + 1 = 7, so a(79) = 7.

Cf. A007094, A053829, A055017, A065359, A065368, A346688, A346689, A346690, A346691, A346732.

nmax = 104; A[] = 0; Do[A[x] = x (1 + 2 x + 3 x^2 + 4 x^3 + 5 x^4 + 6 x^5 + 7 x^6)/(1 - x^8) - (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7) A[x^8] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Table[n + 9 Sum[(-1)^k Floor[n/8^k], {k, 1, Floor[Log[8, n]]}], {n, 0, 104}]

from sympy.ntheory.digits import digits
def a(n):
    return sum(bi*(-1)**k for k, bi in enumerate(digits(n, 8)[1:][::-1]))
print([a(n) for n in range(105)]) # Michael S. Branicky, Jul 31 2021

G.f. A(x) satisfies: A(x) = x * (1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6) / (1 - x^8) - (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7) * A(x^8).

a(n) = n + 9 * Sum_{k>=1} (-1)^k * floor(n/8^k).

A053843 (Sum of digits of n written in base 8) modulo 8.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 0, 2, 3, 4, 5, 6, 7, 0, 1, 3, 4, 5, 6, 7, 0, 1, 2, 4, 5, 6, 7, 0, 1, 2, 3, 5, 6, 7, 0, 1, 2, 3, 4, 6, 7, 0, 1, 2, 3, 4, 5, 7, 0, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 0, 2, 3, 4, 5, 6, 7, 0, 1, 3, 4, 5, 6, 7, 0, 1, 2, 4, 5, 6, 7, 0, 1, 2, 3, 5, 6, 7, 0, 1, 2, 3, 4, 6

Offset: 0

Henry Bottomley, Mar 28 2000

a(n) is the seventh row of the array in A141803. - Andrey Zabolotskiy, May 18 2016

G. C. Greubel, Table of n, a(n) for n = 0..5000
Robert Walker, Self Similar Sloth Canon Number Sequences

Cf. A010877, A053829, A141803.

Cf. A010060, A053837-A053844.

Table[Mod[Plus @@ IntegerDigits[n, 8], 8], {n, 0, 50}] (* G. C. Greubel, Nov 02 2017 *)

a(n) = A010877(A053829(n)). - Andrey Zabolotskiy, May 18 2016

cp's OEIS Frontend

A245355 Sum of digits of n written in fractional base 8/5.

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A010070 Base 8 self or Colombian numbers (not of form k + sum of base 8 digits of k).

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A053831 Sum of digits of n written in base 11.

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A173525 a(n) = 1 + A053824(n-1), where A053824 = sum of digits in base 5.

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A173528 a(n) = 1 + sum of digits of n-1 written in base 8.

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A054897 a(n) = Sum_{k>0} floor(n/8^k).

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