A031076 Write n in base 9 and juxtapose.

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

Offset

1,2

Comments

An irregular table in which the n-th row lists the base-9 digits of n. - Jason Kimberley, Dec 07 2012

The base-9 Champernowne constant: it is normal in base 9. - Jason Kimberley, Dec 07 2012

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Mathematica

Flatten@ IntegerDigits[ Range@ 55, 9] (* 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[#, 9] &, 105] (* Robert G. Wilson v, Jul 01 2014 *)

Prog

(Magma) &cat[Reverse(IntegerToSequence(n, 9)):n in[1..31]]; // Jason Kimberley, Dec 07 2012
(Haskell)
a031076 n = a031076_list !! (n-1)
a031076_list = concat $ map reverse $ tail a031087_tabf
-- Reinhard Zumkeller, Jul 07 2015
(Python)
from itertools import count, chain, islice
from sympy.ntheory.factor_ import digits
def A031076_gen(): return chain.from_iterable(digits(m, 9)[1:] for m in count(1))
A031076_list = list(islice(A031076_gen(), 30)) # Chai Wah Wu, Jan 07 2022
(Python)
from gmpy2 import digits
from oeis_sequences.OEISsequences import bisection, bsearch
def A031076(n):
    def g(x): return x+(m:=len(digits(x, 9)))*(x+1)-9*(9**(m-1)-1>>3)
    def f(x): return n+1+bsearch(g, x)
    return int((s:=digits(a:=bisection(f, n+1, n+1)-n, 9))[n-1-a*(k:=len(s))+(9**k-1>>3)]) # 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), A031035 and A054634 (b=8), this sequence (b=9), A007376 and A033307 (b=10). - Jason Kimberley, Dec 06 2012

Cf. A031087, A007095.

Sequence in context: A265524 A256299 A256289 * A346732 A321999 A228822

Adjacent sequences: A031073 A031074 A031075 * A031077 A031078 A031079

Keyword

nonn,base,cons,easy,tabf

Author

Clark Kimberling

Status

approved