A031035 Write n in base 8 and juxtapose.

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

Offset

1,2

Comments

Apart from the initial term, identical to A054634.

Should not be merged with A054634 because there are many sequences which depend on this sequence 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

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

seq(op(ListTools:-Reverse(convert(n, base, 8))), n=1..100); # Robert Israel, Nov 12 2024

Mathematica

Flatten[ IntegerDigits[ Range[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] (* Robert G. Wilson v, Jun 29 2014 *)

Prog

(Magma) &cat[Reverse(IntegerToSequence(n, 8)):n in[1..31]]; // Jason Kimberley, Dec 07 2012
(Python)
from itertools import count, islice
from sympy.ntheory.factor_ import digits
def A031035_gen(): return (d for m in count(1) for d in digits(m, 8)[1:])
A031035_list = list(islice(A031035_gen(), 30)) # Chai Wah Wu, Jan 07 2022
(Python)
from oeis_sequences.OEISsequences import bisection, bsearch
def A031035(n):
    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

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), this sequence and A054634 (b=8), A031076 (b=9), A007376 and A033307 (b=10). - Jason Kimberley, Dec 06 2012

Cf. A007094.

Sequence in context: A265522 A256298 A256308 * A054634 A346731 A255828

Adjacent sequences: A031032 A031033 A031034 * A031036 A031037 A031038

Keyword

nonn,base,cons,easy,tabf

Author

Clark Kimberling

Status

approved