A030998 Write n in base 7 and juxtapose.

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

Offset

0,3

Comments

An irregular table in which the n-th row lists the base-7 digits of n. - Jason Kimberley, Dec 07 2012

The base-7 Champernowne constant: it is normal in base 7. - Jason Kimberley, Dec 07 2012

Links

Table of n, a(n) for n=0..90.

Mathematica

Flatten[IntegerDigits[#, 7]&/@Range[0, 60]]  (* Harvey P. Dale, Mar 04 2011 *)
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[#, 7] &, 105, 0] (* Robert G. Wilson v, Jun 29 2014 *)

Prog

(Magma) [0]cat &cat[Reverse(IntegerToSequence(n, 7)):n in[1..31]]; // Jason Kimberley, Dec 07 2012
(Python)
from itertools import count, chain, islice
from sympy.ntheory.factor_ import digits
def A030998_gen(): return chain.from_iterable(digits(m, 7)[1:] for m in count(0))
A030998_list = list(islice(A030998_gen(), 30)) # Chai Wah Wu, Jan 07 2022
(Python)
from gmpy2 import digits
from oeis_sequences.OEISsequences import bisection, bsearch
def A030998(n):
    if n == 0: return 0
    def g(x): return x+(m:=len(digits(x, 7)))*(x+1)-7*(7**(m-1)-1)//6
    def f(x): return n+1+bsearch(g, x)
    return int((s:=digits(a:=bisection(f, n+1, n+1)-n, 7))[n-1-a*(k:=len(s))+(7**k-1)//6]) # 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), this sequence (b=7), A031035 and A054634 (b=8), A031076 (b=9), A007376 and A033307 (b=10). - Jason Kimberley, Dec 06 2012

Cf. A007093.

Sequence in context: A265520 A256297 A256307 * A346691 A255827 A277545

Adjacent sequences: A030995 A030996 A030997 * A030999 A031000 A031001

Keyword

nonn,base,cons,easy,tabf

Author

Clark Kimberling

Status

approved