A007095 -id:A007095 - cp's OEIS frontend

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

Clark Kimberling

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

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

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.

a031076 n = a031076_list !! (n-1)
a031076_list = concat $ map reverse $ tail a031087_tabf
-- Reinhard Zumkeller, Jul 07 2015

&cat[Reverse(IntegerToSequence(n,9)):n in[1..31]]; // Jason Kimberley, Dec 07 2012

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 *)

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

A052383 Numbers without 1 as a digit.

Original entry on oeis.org

0, 2, 3, 4, 5, 6, 7, 8, 9, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89

Offset: 1

Henry Bottomley, Mar 13 2000

For each k in {1, 2, ..., 29, 30, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43} there exists at least an m such that m^k is 1-less. If m^k is 1-less then (10*m)^k, (100*m)^k, (1000*m)^k, ... are also 1-less. Therefore for each of these numbers k there exist infinitely many k-th powers in this sequence. - Mohammed Yaseen, Apr 17 2023

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
M. F. Hasler, Numbers avoiding certain digits, OEIS Wiki, Jan 12 2020.
Index entries for 10-automatic sequences.

Cf. A004176, A004720, A011531 (complement), A038603 (subset of primes), A082830 (Kempner series), A248518, A248519.

Cf. A052382 (without 0), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).

a052383 = f . subtract 1 where
   f 0 = 0
   f v = 10 * f w + if r > 0 then r + 1 else 0  where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014

[ n: n in [0..89] | not 1 in Intseq(n) ];  // Bruno Berselli, May 28 2011

M:= 3: # to get all terms with up to M digits
B:= {$2..9}: A:= B union {0}:
for m from 1 to M do
B:= map(b -> seq(10*b+j,j={0,$2..9}), B);
A:= A union B;
od:
sort(convert(A,list)); # Robert Israel, Jan 11 2016
# second program:
A052383 := proc(n)
      option remember;
      if n = 1 then
        0;
    else
        for a from procname(n-1)+1 do
            if nops(convert(convert(a,base,10),set) intersect {1}) = 0 then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Jul 31 2016
# third Maple program:
a:= proc(n) local l, m; l, m:= 0, n-1;
      while m>0 do l:= (d->
        `if`(d=0, 0, d+1))(irem(m, 9, 'm')), l
      od; parse(cat(l))/10
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 01 2016

ban1Q[n_] := FreeQ[IntegerDigits[n], 1] == True; Select[Range[0, 89], ban1Q[#] &] (* Jayanta Basu, May 17 2013 *)
Select[Range[0, 99], DigitCount[#, 10, 1] == 0 &] (* Alonso del Arte, Jan 12 2020 *)

a(n)=my(v=digits(n,9));for(i=1,#v,if(v[i],v[i]++));subst(Pol(v),'x,10) \\ Charles R Greathouse IV, Oct 04 2012

apply( {A052383(n)=fromdigits(apply(d->d+!!d, digits(n-1, 9)))}, [1..99]) \\ Defines the function and computes it for indices 1..99 (check & illustration)
select( {is_A052383(n)=!setsearch(Set(digits(n)), 1)}, [0..99]) \\ Define the characteristic function is_A; as illustration, select the terms in [0..99]
next_A052383(n, d=digits(n+=1))={for(i=1, #d, d[i]==1&& return((1+n\d=10^(#d-i))*d)); n} \\ Successor function: efficiently skip to the next a(k) > n. Used in A038603.  - M. F. Hasler, Jan 11 2020

from itertools import count, islice, product
def A052383(): # generator of terms
    yield 0
    for digits in count(1):
        for f in "23456789":
            for r in product("023456789", repeat=digits-1):
                yield int(f+"".join(r))
print(list(islice(A052383(), 72))) # Michael S. Branicky, Oct 15 2023

from gmpy2 import digits
def A052383(n): return int(''.join(str(int(d)+(d!='0')) for d in digits(n-1,9))) # Chai Wah Wu, Jun 28 2025

(0 to 99).filter(.toString.indexOf('1') == -1) // _Alonso del Arte, Jan 12 2020

seq 0 1000 | grep -v 1; # Joerg Arndt, May 29 2011

a(1) = 1, a(n + 1) = f(a(n) + 1, a(n) + 1) where f(x, y) = if x < 10 and x <> 1 then y else if x mod 10 = 1 then f(y + 1, y + 1) else f(floor(x/10), y). - Reinhard Zumkeller, Mar 02 2008
a(n) is the replacement of all nonzero digits d by d + 1 in the base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014
Sum_{k>1} 1/a(k) = A082830 = 16.176969... (Kempner series). - Bernard Schott, Jan 12 2020

Offset changed by Reinhard Zumkeller, Oct 07 2014

A031087 Triangle T(n,k): write n in base 9, reverse order of digits.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling

Reinhard Zumkeller, Rows n = 0..1000 of triangle, flattened

Cf. A030308, A030341, A030386, A031235, A030567, A031007, A031045, A031298 for the base-2 to base-10 analogs.

Cf. A031076, A007095.

a031087 n k = a031087_row n !! (k-1)
a031087_row n | n < 9     = [n]
              | otherwise = m : a031087_row n' where (n',m) = divMod n 9
a031087_tabf = map a031087_row [0..]
-- Reinhard Zumkeller, Jul 07 2015

A031087(n, k=-1)=/*k<0&&error("Flattened sequence not yet implemented.")*/n\9^k%9 \\ Assuming that columns are numbered starting with k=0 as in A030308, A030567 and others. - M. F. Hasler, Jul 21 2013

Initial 0 and better name by Philippe Deléham, Oct 20 2011

A038617 Primes not containing the digit '9'.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 23, 31, 37, 41, 43, 47, 53, 61, 67, 71, 73, 83, 101, 103, 107, 113, 127, 131, 137, 151, 157, 163, 167, 173, 181, 211, 223, 227, 233, 241, 251, 257, 263, 271, 277, 281, 283, 307, 311, 313, 317, 331, 337, 347, 353, 367, 373, 383, 401, 421

Offset: 1

Vasiliy Danilov (danilovv(AT)usa.net), Jul 15 1998

Subsequence of primes of A007095. - Michel Marcus, Feb 22 2015

Maynard proves that this sequence is infinite and in particular contains the expected number of elements up to x, on the order of x^(log 9/log 10)/log x. - Charles R Greathouse IV, Apr 08 2016

Indranil Ghosh, Table of n, a(n) for n = 1..50000
M. F. Hasler, Numbers avoiding certain digits, OEIS wiki, Jan 12 2020.
James Maynard, Primes with restricted digits, arXiv:1604.01041 [math.NT], 2016.
James Maynard and Brady Haran, Primes without a 7, Numberphile video (2019).
Index to entries for primes with digits in a given set

Intersection of A000040 (primes) and A007095 (numbers with no digit 9).
Primes having no digit d = 0..9 are A038618, A038603, A038604, A038611, A038612, A038613, A038614, A038615, A038616, and this sequence, respectively.
Primes with other restrictions on digits: A106116, A156756.

[ p: p in PrimesUpTo(500) | not 9 in Intseq(p) ]; // Bruno Berselli, Aug 08 2011

Select[Prime[Range[1000]], DigitCount[ # ][[9]] == 0 &] (* Stefan Steinerberger, May 20 2006 *)

lista(nn)=forprime(p=2, nn, if (!vecsearch(vecsort(digits(p),,8), 9), print1(p, ", "));); \\ Michel Marcus, Feb 22 2015

lista(nn) = forprime (p=2, nn, if (vecmax(digits(p)) != 9, print1(p, ", "))); \\ Michel Marcus, Apr 06 2016

next_A038617(n)=until((n=nextprime(n+1))==(n=next_A007095(n-1)), ); n \\ M. F. Hasler, Jan 14 2020

from sympy import isprime
i = 1
while i <= 300:
    if "9" not in str(i) and isprime(i):
        print(str(i), end=",")
    i += 1 # Indranil Ghosh, Feb 07 2017

a(n) ~ n^(log 10/log 9) * log(n). - Charles R Greathouse IV, Aug 03 2023

A102683 Number of digits 9 in decimal representation of n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0

Offset: 0

N. J. A. Sloane, Feb 03 2005

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A007095, A011539, A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564, A235049.
Cf. A102684 (partial sums).
Cf. A000120, A000788, A023416, A059015 (for base 2).

a102683 =  length . filter (== '9') . show
-- Reinhard Zumkeller, Dec 29 2011

p:=proc(n) local b,ct,j: b:=convert(n,base,10): ct:=0: for j from 1 to nops(b) do if b[j]>=9 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(p(n),n=0..116); # Emeric Deutsch, Feb 23 2005

a[n_] := DigitCount[n, 10, 9]; Array[a, 100, 0] (* Amiram Eldar, Jul 24 2023 *)

a(A007095(n)) = 0; a(A011539(n)) > 0. - Reinhard Zumkeller, Dec 29 2011
From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = Sum_{j=1..m+1} (floor(n/10^j + 1/10) - floor(n/10^j)), where m=floor(log_10(n)).
G.f.: g(x) = (1/(1-x))*Sum_{j>=0} (x^(9*10^j) - x^(10*10^j))/(1-x^10^(j+1)). (End)
a(A235049(n)) = 0. - Reinhard Zumkeller, Apr 16 2014

More terms from Emeric Deutsch, Feb 23 2005

A082838 Decimal expansion of Kempner series Sum_{k>=1, k has no digit 9 in base 10} 1/k.

Original entry on oeis.org

2, 2, 9, 2, 0, 6, 7, 6, 6, 1, 9, 2, 6, 4, 1, 5, 0, 3, 4, 8, 1, 6, 3, 6, 5, 7, 0, 9, 4, 3, 7, 5, 9, 3, 1, 9, 1, 4, 9, 4, 4, 7, 6, 2, 4, 3, 6, 9, 9, 8, 4, 8, 1, 5, 6, 8, 5, 4, 1, 9, 9, 8, 3, 5, 6, 5, 7, 2, 1, 5, 6, 3, 3, 8, 1, 8, 9, 9, 1, 1, 1, 2, 9, 4, 4, 5, 6, 2, 6, 0, 3, 7, 4, 4, 8, 2, 0, 1, 8, 9, 8, 9, 9, 0, 9

Offset: 2

Robert G. Wilson v, Apr 14 2003

Numbers with a digit 9 (A011539) have asymptotic density 1, i.e., here almost all terms are removed from the harmonic series, which makes convergence less surprising. See A082839 (the analog for digit 0) for more information about such so-called Kempner series. - M. F. Hasler, Jan 13 2020

			22.920676619264150348163657094375931914944762436998481568541998356... - _Robert G. Wilson v_, Jun 01 2009

Julian Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 34.

Robert Baillie, Sums of reciprocals of integers missing a given digit, Amer. Math. Monthly, 86 (1979), 372-374.
Robert Baillie, Summing the curious series of Kempner and Irwin, arXiv:0806.4410 [math.CA], 2008-2015.
Aubrey J. Kempner, A Curious Convergent Series, American Mathematical Monthly, volume 21, number 2, February 1914, pages 48-50. Or JSTOR.
Eric Weisstein's World of Mathematics, Kempner Series.
Wikipedia, Kempner series
Wolfram Library Archive, KempnerSums.nb (8.6 KB) - Mathematica Notebook, Summing Kempner's Curious (Slowly-Convergent) Series

Cf. A002387, A007095 (numbers with no '9'), A011539 (numbers with a '9'), A024101.

Cf. A082830 .. A082839 (analog for digits 1, ..., 8 and 0), A140502.

(* see the Mmca in Wolfram Library Archive link *)

Equals Sum_{k in A007095\{0}} 1/k, where A007095 = numbers with no digit 9. - M. F. Hasler, Jan 15 2020

More terms from Robert G. Wilson v, Apr 14 2009
More terms from Robert G. Wilson v, Jun 01 2009
Minor edits by M. F. Hasler, Jan 13 2020

A052405 Numbers without 3 as a digit.

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89

Offset: 1

Henry Bottomley, Mar 13 2000

This sequence also represents the minimal number of straight lines of a covering tree to cover n X n points arranged in a symmetrical grid. - Marco Ripà, Sep 20 2018

			22 has no 3s among its digits, hence it is in the sequence.
23 has one 3 among its digits, hence it is not in the sequence.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
M. F. Hasler, Numbers avoiding certain digits, OEIS Wiki, Jan 12 2020.
Index entries for 10-automatic sequences.

Cf. A004178, A004722, A038611 (subset of primes), A082832 (Kempner series).
Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).
Cf. A011533 (complement).

a052405 = f . subtract 1 where
   f 0 = 0
   f v = 10 * f w + if r > 2 then r + 1 else r  where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014

[ n: n in [0..89] | not 3 in Intseq(n) ];  // Bruno Berselli, May 28 2011

a:= proc(n) local l, m; l, m:= 0, n-1;
      while m>0 do l:= (d->
        `if`(d<3, d, d+1))(irem(m, 9, 'm')), l
      od; parse(cat(l))/10
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 01 2016

Select[Range[0, 89], DigitCount[#, 10, 3] == 0 &] (* Alonso del Arte, Oct 16 2012 *)

is(n)=n=digits(n);for(i=1,#n,if(n[i]==3,return(0)));1 \\ Charles R Greathouse IV, Oct 16 2012
apply( {A052405(n)=fromdigits(apply(d->d+(d>2),digits(n-1,9)))}, [1..99]) \\ a(n)
next_A052405(n, d=digits(n+=1))={for(i=1, #d, d[i]==3&& return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n. Used in A038611. \\ M. F. Hasler, Jan 11 2020

from gmpy2 import digits
def A052405(n): return int(digits(n-1,9).translate(str.maketrans('345678','456789'))) # Chai Wah Wu, Jun 28 2025

seq 0 1000 | grep -v 3; # Joerg Arndt, May 29 2011

a(n) >> n^k with k = log(10)/log(9) = 1.0479.... - Charles R Greathouse IV, Oct 16 2012
a(n) = replace digits d > 2 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014
Sum_{n>1} 1/a(n) = A082832 = 20.569877... (Kempner series). - Bernard Schott, Jan 12 2020, edited by M. F. Hasler, Jan 14 2020

Offset changed by Reinhard Zumkeller, Oct 07 2014

A052413 Numbers without 5 as a digit.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89

Offset: 1

Henry Bottomley, Mar 13 2000

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
M. F. Hasler, Numbers avoiding certain digits, OEIS wiki, Jan 12 2020
Index entries for 10-automatic sequences.

Cf. A004180, A004724, A038613 (subset of primes), A082834 (Kempner series).

Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).

a052413 = f . subtract 1 where
f 0 = 0
f v = 10 * f w + if r > 4 then r + 1 else r where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014

[ n: n in [0..89] | not 5 in Intseq(n) ]; // Bruno Berselli, May 28 2011

a:= proc(n) local l, m; l, m:= 0, n-1;
      while m>0 do l:= (d->
        `if`(d<5, d, d+1))(irem(m, 9, 'm')), l
      od; parse(cat(l))/10
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 01 2016

Select[Range[100],!MemberQ[IntegerDigits[#],5]&] (* Harvey P. Dale, Feb 20 2013 *)

apply( {A052413(n)=fromdigits(apply(d->d+(d>4),digits(n-1,9)))}, [1..99]) \\ a(n)
select( {is_A052413(n)=!setsearch(Set(digits(n)),5)}, [0..99]) \\ used in A038613
next_A052413(n, d=digits(n+=1))={for(i=1,#d, d[i]==5&&return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n; used in A038613. - M. F. Hasler, Jan 11 2020

# see the OEIS wiki page (cf. LINKS) for more programs
def A052413(n): n-=1; return sum(n//9**e%9*6//5*10**e for e in range(math.ceil(math.log(n+1,9)))) # M. F. Hasler, Jan 13 2020

from gmpy2 import digits
def A052413(n): return int(digits(n-1,9).translate(str.maketrans('5678','6789'))) # Chai Wah Wu, Jun 28 2025

seq 0 1000 | grep -v 5; # Joerg Arndt, May 29 2011

a(n) = replace digits d > 4 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014

Sum_{k>1} 1/a(n) = A082834 = 21.8346008... (Kempner series). - Bernard Schott, Jan 12 2020, edited by M. F. Hasler, Jan 13 2020

Offset changed by Reinhard Zumkeller, Oct 07 2014

A100973 Integers that are Rhonda numbers to base 9.

Original entry on oeis.org

15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857, 77142, 83334, 83694, 96448, 97944, 106575, 108273, 117624, 125952, 138966, 141204, 144236, 153318, 158417, 159424, 188529, 188598, 189350, 192000, 192126, 196652, 202350, 203320, 205390, 246675, 247632

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 25 2004

See sequence A099542 for definition of Rhonda numbers and for some links.

			The product of the base 9 digits of 15540 is 2*3*2*7*6=504, the sum of the prime factors of 15540 is 2*2+3+5+7+37=56 and 504=9*56. So 15540 is a Rhonda number to base 9.

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Rhonda Number

Cf. Rhonda numbers to other bases: A100968 (base 4), A100969 (base 6), A100970 (base 8), A099542 (base 10), A100971 (base 12), A100972 (base 14), A100974 (base 15), A100975 (base 16), A255735 (base 18), A255732 (base 20), A255736 (base 30), A255731 (base 60), see also A255872.
Cf. A001414, A027746, A007095, subsequence of A255808.
Column k=4 of A291925.

a100973 n = a100973_list !! (n-1)
a100973_list = filter (rhonda 9) a255808_list
-- Function rhonda as in A099542.
-- Reinhard Zumkeller, Mar 08 2015

A100973Q[k_] := Times @@ IntegerDigits[k, 9] == 9*Total[Times @@@ FactorInteger[k]];
Select[Range[250000], A100973Q] (* Paolo Xausa, Jul 01 2025 *)

A052414 Numbers without 6 as a digit.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89

Offset: 1

Henry Bottomley, Mar 13 2000

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
M. F. Hasler, Numbers avoiding certain digits OEIS wiki, Jan 12 2020.
Index entries for 10-automatic sequences.

Cf. A004181, A004725, A038614 (subset of primes), A082835 (Kempner series).

Cf. A052382 (without 0), A052383 (without 1), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052419 (without 7), A052421 (without 8), A007095 (without 9).

a052414 = f . subtract 1 where
f 0 = 0
f v = 10 * f w + if r > 5 then r + 1 else r where (w, r) = divMod v 9
-- Reinhard Zumkeller, Oct 07 2014

[ n: n in [0..89] | not 6 in Intseq(n) ]; // Bruno Berselli, May 28 2011

a:= proc(n) local l, m; l, m:= 0, n-1;
      while m>0 do l:= (d->
        `if`(d<6, d, d+1))(irem(m, 9, 'm')), l
      od; parse(cat(l))/10
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Aug 01 2016

Select[Range[0,100],DigitCount[#,10,6]==0&] (* Harvey P. Dale, Jun 20 2013 *)

lista(nn)=for (n=0, nn, if (!vecsearch(vecsort(digits(n),,8), 6), print1(n, ", "));); \\ Michel Marcus, Feb 22 2015

/* See OEIS wiki page (cf. LINKS) for more programs */
apply( {A052414(n)=fromdigits(apply(d->d+(d>5),digits(n-1,9)))}, [1..99]) \\ a(n)
select( {is_A052414(n)=!setsearch(Set(digits(n)),6)}, [0..99]) \\ used in A038614
next_A052414(n, d=digits(n+=1))={for(i=1,#d, d[i]==6&&return((1+n\d=10^(#d-i))*d)); n} \\ least a(k) > n, used in A038614. - M. F. Hasler, Jan 11 2020

from gmpy2 import digits
def A052414(n): return int(digits(n-1,9).translate(str.maketrans('678','789'))) # Chai Wah Wu, Jun 28 2025

seq 0 1000 | grep -v 6; # Joerg Arndt, May 29 2011

a(n) = replace digits d > 5 by d + 1 in base-9 representation of n - 1. - Reinhard Zumkeller, Oct 07 2014

Sum_{k>1} 1/a(k) = A082835 = 22.205598... (Kempner series). - Bernard Schott, Jan 12 2020, edited by M. F. Hasler, Jan 13 2020

Offset changed by Reinhard Zumkeller, Oct 07 2014

cp's OEIS Frontend

A031076 Write n in base 9 and juxtapose.

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A052383 Numbers without 1 as a digit.

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A031087 Triangle T(n,k): write n in base 9, reverse order of digits.

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A038617 Primes not containing the digit '9'.

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A102683 Number of digits 9 in decimal representation of n.

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A082838 Decimal expansion of Kempner series Sum_{k>=1, k has no digit 9 in base 10} 1/k.

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