A054634 Champernowne sequence: write n in base 8 and juxtapose.

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

Offset

0,3

Comments

Apart from the initial term, identical to A031035.

Should not be merged with A031035 because there are many sequences which depend on the latter starting with a 1. - N. J. A. Sloane, Jan 30 2010

An irregular table in which the n-th row lists the base-8 digits of n. - Jason Kimberley, Dec 07 2012

The base-8 Champernowne constant: it is normal in base 8. - Jason Kimberley, Dec 07 2012

Links

Table of n, a(n) for n=0..98.

Mathematica

Flatten[ IntegerDigits[ Range[0, 40], 8]] (* or *)
almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; Array[ almostNatural[#, 8] &, 105, 0] (* Robert G. Wilson v, Jun 29 2014 *)

Prog

(Magma) [0]cat &cat[Reverse(IntegerToSequence(n, 8)):n in[1..31]]; // Jason Kimberley, Dec 07 2012
(Python)
from itertools import count, chain, islice
from sympy.ntheory.factor_ import digits
def A054634_gen(): return chain.from_iterable(digits(m, 8)[1:] for m in count(0))
A054634_list = list(islice(A054634_gen(), 30)) # Chai Wah Wu, Jan 07 2022
(Python)
from oeis_sequences.OEISsequences import bisection, bsearch
def A054634(n):
    if n == 0: return 0
    def g(x): return x+(m:=(x.bit_length()+2)//3)*(x+1)-((1<<3*(m-1))-1<<3)//7 if x else 1
    def f(x): return n+1+bsearch(g, x)
    return int((s:=oct(a:=bisection(f, n+1, n+1)-n)[2:])[n-1-a*(k:=len(s))+((1<<3*k)-1)//7]) # Chai Wah Wu, Mar 02 2026

Crossrefs

Cf. A007376, A030190, A007094.

Tables in which the n-th row lists the base b digits of n: A030190 and A030302 (b=2), A003137 and A054635 (b=3), A030373 (b=4), A031219 (b=5), A030548 (b=6), A030998 (b=7), A031035 and this sequence (b=8), A031076 (b=9), A007376 and A033307 (b=10). - Jason Kimberley, Dec 06 2012

Sequence in context: A256298 A256308 A031035 * A346731 A255828 A277546

Adjacent sequences: A054631 A054632 A054633 * A054635 A054636 A054637

Keyword

nonn,base,cons,easy,tabf

Author

N. J. A. Sloane, Apr 16 2000

Status

approved