A214676 -id:A214676 - cp's OEIS frontend

A052382 Numbers without 0 in the decimal expansion, colloquial 'zeroless numbers'.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 111, 112, 113

Offset: 1

Henry Bottomley, Mar 13 2000

The entries 1 to 79 match the corresponding subsequence of A043095, but then 81, 91-98, 100, 102, etc. are only in one of the two sequences. - R. J. Mathar, Oct 13 2008
Complement of A011540; A168046(a(n)) = 1; A054054(a(n)) > 0; A007602, A038186, A038618, A052041, A052043, and A052045 are subsequences. - Reinhard Zumkeller, Apr 25 2012, Apr 07 2011, Dec 01 2009
a(n) = n written in base 9 where zeros are not allowed but nines are. The nine distinct digits used are 1, 2, 3, ..., 9 instead of 0, 1, 2, ..., 8. To obtain this sequence from the "canonical" base 9 sequence with zeros allowed, just replace any 0 with a 9 and then subtract one from the group of digits situated on the left. For example, 9^3 = 729 (10) (in base 10) = 1000 (9) (in base 9) = 889 (9-{0}) (in base 9 without zeros) because 100 (9) = [9-1]9 = 89 (9-{0}) and thus 1000 (9) = [89-1]9 = 889 (9-{0}). - Robin Garcia, Jan 15 2014
From Hieronymus Fischer, May 28 2014: (Start)
Inversion: Given a term m, the index n such that a(n) = m can be calculated by A052382_inverse(m) = m - sum_{1<=j<=k} floor(m/10^j)*9^(j-1), where k := floor(log_10(m)) [see Prog section for an implementation in Smalltalk].
Example 1: A052382_inverse(137) = 137 - (floor(137/10) + floor(137/100)*9) = 137 - (13*1 + 1*9) = 137 - 22 = 115.
Example 2: A052382_inverse(4321) = 4321 - (floor(4321/10) + floor(4321/100)*9 + floor(4321/1000)*81) = 4321 - (432*1 + 43*9 + 4*81) = 4321 - (432 + 387 + 324) = 3178. (End)
The sum of the reciprocals of these numbers from a(1)=1 to infinity, called the Kempner series, is convergent towards a limit: 23.103447... whose decimal expansion is in A082839. - Bernard Schott, Feb 23 2019
Integer n > 0 is encoded using bijective base-9 numeration, see Wikipedia link below. - Alois P. Heinz, Feb 16 2020

			For k >= 0, a(10^k) = (1, 11, 121, 1331, 14641, 162151, 1783661, 19731371, ...) = A325203(k). - _Hieronymus Fischer_, May 30 2012 and Jun 06 2012; edited by _M. F. Hasler_, Jan 13 2020

Paul Halmos, "Problems for Mathematicians, Young and Old", Dolciani Mathematical Expositions, 1991, p. 258.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
K. Mahler, On the generating function of the integers with a missing digit, J. Indian Math. Soc. 15A (1951), 34-40.
Eric Weisstein's World of Mathematics, Kempner Series.
Eric Weisstein's World of Mathematics, Zerofree
Wikipedia, Bijective numeration
Index entries for 10-automatic sequences.

Cf. A004719, A052040, different from A067251.
Cf. A055640, A046034, A007931, A007932, A084544, A084545.
Column k=9 of A214676.
Cf. A011540 (complement), A043489, A054054, A168046.
Cf. A052383 (without 1), A052404 (without 2), A052405 (without 3), A052406 (without 4), A052413 (without 5), A052414 (without 6), A052419 (without 7), A052421 (without 8), A007095 (without 9).
Zeroless numbers in some other bases <= 10: A000042 (base 2), A032924 (base 3), A023705 (base 4), A248910 (base 6), A255805 (base 8), A255808 (base 9).
Cf. A082839 (sum of reciprocals).
Cf. A038618 (subset of primes)
Subsequences: A007602, A038186, A052041, A052043, A052045, A059405, A066484, A099542.

a052382 n = a052382_list !! (n-1)
a052382_list = iterate f 1 where
f x = 1 + if r < 9 then x else 10 * f x' where (x', r) = divMod x 10
-- Reinhard Zumkeller, Mar 08 2015, Apr 07 2011

[ n: n in [1..114] | not 0 in Intseq(n) ]; // Bruno Berselli, May 28 2011

a:= proc(n) local d, l, m; m:= n; l:= NULL;
      while m>0 do d:= irem(m, 9, 'm');
        if d=0 then d:=9; m:= m-1 fi;
        l:= d, l
      od; parse(cat(l))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jan 11 2015
is_zeroless := n -> not is(0 in convert(n, base, 10)):
select(is_zeroless, [seq(1..113)]);  # Peter Luschny, Jun 20 2025

A052382 = Select[Range[100], DigitCount[#, 10, 0] == 0 &] (* Alonso del Arte, Mar 10 2011 *)

select( {is_A052382(n)=n&&vecmin(digits(n))}, [0..111]) \\ actually: is_A052382 = (bool) A054054. - M. F. Hasler, Jan 23 2013, edited Jan 13 2020

a(n) = for (w=0, oo, if (n >= 9^w, n -= 9^w, return ((10^w-1)/9 + fromdigits(digits(n, 9))))) \\ Rémy Sigrist, Jul 26 2017

apply( {A052382(n,L=logint(n,9))=fromdigits(digits(n-9^L>>3,9))+10^L\9}, [1..100])
next_A052382(n, d=digits(n+=1))={for(i=1, #d, d[i]|| return(n-n%(d=10^(#d-i+1))+d\9)); n} \\ least a(k) > n. Used in A038618.
( {A052382_vec(n,M=1)=M--;vector(n, i, M=next_A052382(M))} )(99) \\ n terms >= M
\\ See OEIS Wiki page (cf. LINKS) for more programs. - M. F. Hasler, Jan 11 2020

A052382 = [n for n in range(1,10**5) if not str(n).count('0')]
# Chai Wah Wu, Aug 26 2014

from sympy import integer_log
def A052382(n):
    m = integer_log(k:=(n<<3)+1,9)[0]
    return sum((1+(k-9**m)//(9**j<<3)%9)*10**j for j in range(m)) # Chai Wah Wu, Jun 27 2025

A052382
"Answers the n-th term of A052382, where n is the receiver."
^self zerofree: 10
A052382_inverse
"Answers that index n which satisfy A052382(n) = m, where m is the receiver.”
^self zerofree_inverse: 10
zerofree: base
"Answers the n-th zerofree number in base base, where n is the receiver. Valid for base > 2.
Usage: n zerofree: b [b = 10 for this sequence]
Answer: a(n)"
| n m s c bi ci d |
n := self.
c := base - 1.
m := (base - 2) * n + 1 integerFloorLog: c.
d := n - (((c raisedToInteger: m) - 1)//(base - 2)).
bi := 1.
ci := 1.
s := 0.
1 to: m
do:
[:i |
s := (d // ci \\ c + 1) * bi + s.
bi := base * bi.
ci := c * ci].
^s
zerofree_inverse: base
"Answers the index n such that the n-th zerofree number in base base is = m, where m is the receiver. Valid for base > 2.
Usage: m zerofree_inverse: b [b = 10 for this sequence]
Answer: n"
| m p q s |
m := self.
s := 0.
p := base.
q := 1.
[p < m] whileTrue:
[s := m // p * q + s.
p := base * p.
q := (base - 1) * q].
^m - s
"by Hieronymus Fischer, May 28 2014"

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

a(n+1) = f(a(n)) with f(x) = 1 + if x mod 10 < 9 then x else 10*f([x/10]). - Reinhard Zumkeller, Nov 15 2009
From Hieronymus Fischer, Apr 30, May 30, Jun 08 2012, Feb 17 2019: (Start)
a(n) = Sum_{j=0..m-1} (1 + b(j) mod 9)*10^j, where m = floor(log_9(8*n + 1)), b(j) = floor((8*n + 1 - 9^m)/(8*9^j)).
Also: a(n) = Sum_{j=0..m-1} (1 + A010878(b(j)))*10^j.
a(9*n + k) = 10*a(n) + k, k=1..9.
Special values:
a(k*(9^n - 1)/8) = k*(10^n - 1)/9, k=1..9.
a((17*9^n - 9)/8) = 2*10^n - 1.
a((9^n - 1)/8 - 1) = 10^(n-1) - 1, n > 1.
Inequalities:
a(n) <= (1/9)*((8*n+1)^(1/log_10(9)) - 1), equality holds for n=(9^k-1)/8, k>0.
a(n) > (1/10)*((8*n+1)^(1/log_10(9)) - 1), n > 0.
Lower and upper limits:
lim inf a(n)/10^log_9(8*n) = 1/10, for n -> infinity.
lim inf a(n)/n^(1/log_10(9)) = 8^(1/log_10(9))/10, for n -> infinity.
lim sup a(n)/10^log_9(8*n) = 1/9, for n -> infinity.
lim sup a(n)/n^(1/log_10(9)) = 8^(1/log_10(9))/9, for n -> infinity.
G.f.: g(x) = (x^(1/8)*(1-x))^(-1) Sum_{j>=0} 10^j*z(j)^(9/8)*(1 - 10z(j)^9 + 9z(j)^10)/((1-z(j))(1-z(j)^9)), where z(j) = x^9^j.
Also: g(x) = (1/(1-x)) Sum_{j>=0} (1 - 10(x^9^j)^9 + 9(x^9^j)^10)*x^9^j*f_j(x)/(1-x^9^j), where f_j(x) = 10^j*x^((9^j-1)/8)/(1-(x^9^j)^9). Here, the f_j obey the recurrence f_0(x) = 1/(1-x^9), f_(j+1)(x) = 10x*f_j(x^9).
Also: g(x) = (1/(1-x))*((Sum{k=0..8} h_(9,k)(x)) - 9*h_(9,9)(x)), where h_(9,k)(x) = Sum_{j>=0} 10^j*x^((9^(j+1)-1)/8)*x^(k*9^j)/(1-x^9^(j+1)).
Generic formulas for analogous sequences with numbers expressed in base p and only using the digits 1, 2, 3, ... d, where 1 < d < p:
a(n) = Sum_{j=0..m-1} (1 + b(j) mod d)*p^j, where m = floor(log_d((d-1)*n+1)), b(j) = floor(((d-1)*n+1-d^m)/((d-1)*d^j)).
Special values:
a(k*(d^n-1)/(d-1)) = k*(10^n-1)/9, k=1..d.
a(d*((2d-1)*d^(n-1)-1)/(d-1)) = ((d+9)*10^n-d)/9 = 10^n + d*(10^n-1)/9.
a((d^n-1)/(d-1)-1) = d*(10^(n-1)-1)/9, n > 1.
Inequalities:
a(n) <= (10^log_d((d-1)*n+1)-1)/9, equality holds for n = (d^k-1)/(d-1), k > 0.
a(n) > (d/10)*(10^log_d((d-1)*n+1)-1)/9, n > 0.
Lower and upper limits:
lim inf a(n)/10^log_d((d-1)*n) = d/90, for n -> infinity.
lim sup a(n)/10^log_d((d-1)*n) = 1/9, for n -> infinity.
G.f.: g(x) = (1/(1-x)) Sum_{j>=0} (1 - (d+1)(x^d^j)^d + d(x^d^j)^(d+1))*x^d^j*f_j(x)/(1-x^d^j), where f_j(x) = p^j*x^((d^j-1)/(d-1))/(1-(x^d^j)^d). Here, the f_j obey the recursion f_0(x) = 1/(1-x^d), f_(j+1)(x) = px*f_j(x^d).
(End)
A052382 = { n | A054054(n) > 0 }. - M. F. Hasler, Jan 23 2013
From Hieronymus Fischer, Feb 20 2019: (Start)
Sum_{n>=1} (-1)^(n+1)/a(n) = 0.696899720...
Sum_{n>=1} 1/a(n)^2 = 1.6269683705819...
Sum_{n>=1} 1/a(n) = 23.1034479... = A082839. This so-called Kempner series converges very slowly. For the calculation of the sum, it is helpful to use the following fraction of partial sums, which converges rapidly:
lim_{n->infinity} (Sum_{k=p(n)..p(n+1)-1} 1/a(k)) / (Sum_{k=p(n-1)..p(n)-1} 1/a(k)) = 9/10, where p(n) = (9^n-1)/8, n > 1.
(End)

Typos in formula section corrected by Hieronymus Fischer, May 30 2012

Name clarified by Peter Luschny, Jun 20 2025

A214679 A(n,k) = Fibonacci(n) represented in bijective base-k numeration; square array A(n,k), n>=1, k>=1, read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 1, 11, 1, 1, 2, 111, 1, 1, 2, 11, 11111, 1, 1, 2, 3, 21, 11111111, 1, 1, 2, 3, 12, 112, 1111111111111, 1, 1, 2, 3, 11, 22, 221, 111111111111111111111, 1, 1, 2, 3, 5, 14, 111, 1221, 1111111111111111111111111111111111

Offset: 1

Alois P. Heinz, Jul 25 2012

The digit set for bijective base-k numeration is {1, 2, ..., k}.

			Square array A(n,k) begins:
:                     1,    1,   1,   1,   1,  1,  1,  1,  1, ...
:                     1,    1,   1,   1,   1,  1,  1,  1,  1, ...
:                    11,    2,   2,   2,   2,  2,  2,  2,  2, ...
:                   111,   11,   3,   3,   3,  3,  3,  3,  3, ...
:                 11111,   21,  12,  11,   5,  5,  5,  5,  5, ...
:              11111111,  112,  22,  14,  13, 12, 11,  8,  8, ...
:         1111111111111,  221, 111,  31,  23, 21, 16, 15, 14, ...
: 111111111111111111111, 1221, 133, 111,  41, 33, 27, 25, 23, ...

Alois P. Heinz, Antidiagonals n = 1..13
R. R. Forslund, A logical alternative to the existing positional number system, Southwest Journal of Pure and Applied Mathematics, Vol. 1, 1995, 27-29.
Eric Weisstein's World of Mathematics, Zerofree
Wikipedia, Bijective numeration

Columns k=1-9 give: A108047, A085652, A282234, A282235, A282236, A282237, A282238, A282239, A282240.

Cf. A000045, A214676.

with(combinat):
A:= proc(n, b) local d, l, m; m:= fibonacci(n); l:= NULL;
      while m>0 do  d:= irem(m, b, 'm');
        if d=0 then d:=b; m:=m-1 fi;
        l:= d, l
      od; parse(cat(l))
    end:
seq(seq(A(n, 1+d-n), n=1..d), d=1..10);

A[n_, b_] := Module[{d, l, m}, m = Fibonacci@n; l = Nothing; While[m > 0, {m, d} = QuotientRemainder[m, b]; If[d == 0, d = b; m--]; l = {d, l}]; FromDigits @ Flatten @ l];
Table[A[n, d-n+1], {d, 1, 10}, {n, 1, d}] // Flatten (* Jean-François Alcover, May 28 2019, from Maple *)

A(n,k) = A214676(A000045(n),k).

A057436 Contains digits 1 through 6 only.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66, 111, 112, 113, 114, 115, 116, 121, 122, 123, 124, 125, 126, 131, 132, 133, 134, 135, 136, 141, 142, 143

Offset: 1

Thomas Schulze (jazariel(AT)tiscalenet.it), Sep 08 2000

Numbers whose digits can be generated by successively throwing a regular die with the numbers 1..6 and concatenating the results.

			The number 61 can be generated by throwing a die twice and combining the results, but 17 not.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.

Cf. A007092, A214676.

import Data.List (intersect)
a057436 n = a057436_list !! (n-1)
a057436_list = filter (null . (intersect "0789") . show) [1..]
-- Reinhard Zumkeller, Mar 28 2012

Select[Range[200],Max[IntegerDigits[#]]<=6&& DigitCount[#,10,0] ==0&]  (* Harvey P. Dale, Apr 04 2011 *)
FromDigits/@Flatten[Table[Tuples[Range[6],n],{n,3}],1] (* Harvey P. Dale, Jul 26 2015 *)

from itertools import product
A057436_list = [int(''.join(d)) for l in range(1,5) for d in product('123456',repeat=l)] # Chai Wah Wu, Sep 01 2021

a(n+1) = 1 + (if a(n) mod 10 < 6 then a(n) else a(a(n)\10)*10), a(0)=1. - Reinhard Zumkeller, Jul 13 2007

Offset corrected by Reinhard Zumkeller, Aug 16 2011

A258410 Nonnegative integers with an equal number of occurrences of all digits in bijective base-2 numeration.

Original entry on oeis.org

4, 5, 18, 20, 21, 24, 25, 27, 70, 74, 76, 77, 82, 84, 85, 88, 89, 91, 98, 100, 101, 104, 105, 107, 112, 113, 115, 119, 270, 278, 282, 284, 285, 294, 298, 300, 301, 306, 308, 309, 312, 313, 315, 326, 330, 332, 333, 338, 340, 341, 344, 345, 347, 354, 356, 357

Offset: 1

Alois P. Heinz, May 29 2015

			4 = 12_bij2, 5 = 21_bij2, 18 = 1122_bij2, 20 = 1212_bij2.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Wikipedia, Bijective numeration

Cf. A007931, A214676, A257869, A258411.

p:= proc(n) local d, m, r; m:= n; r:= 0;
      while m>0 do d:= irem(m, 2, 'm');
        if d=0 then d:=2; m:= m-1 fi;
        r:= r+x^d
      od;
      simplify(r/(x+x^2))::integer
    end:
a:= proc(n) option remember; local k;
      for k from 1+`if`(n=1, 0, a(n-1)) by 1
      while not p(k) do od; k
    end:
seq(a(n), n=1..70);

A214678 a(n) = n represented in bijective base-8 numeration.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 26, 27, 28, 31, 32, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 71, 72, 73, 74, 75, 76, 77, 78, 81, 82, 83

Offset: 1

Alois P. Heinz, Jul 25 2012

Alois P. Heinz, Table of n, a(n) for n = 1..10000
R. R. Forslund, A logical alternative to the existing positional number system, Southwest Journal of Pure and Applied Mathematics, Vol. 1, 1995, 27-29.
Eric Weisstein's World of Mathematics, Zerofree
Wikipedia, Bijective numeration

Column k=8 of A214676.

a:= proc(n) local d, l, m; m:= n; l:= NULL;
      while m>0 do d:= irem(m, 8, 'm');
        if d=0 then d:=8; m:= m-1 fi;
        l:= d, l
      od; parse(cat(l))
    end:
seq(a(n), n=1..100);

With[{b = 8}, Flatten@ Table[FromDigits[PadLeft[IntegerDigits[k, b], n] /. k_ :> k + 1], {n, 3}, {k, 0, b^n - 1}] ] (* Michael De Vlieger, Sep 16 2023 *)

A214677 a(n) = n represented in bijective base-7 numeration.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 14, 15, 16, 17, 21, 22, 23, 24, 25, 26, 27, 31, 32, 33, 34, 35, 36, 37, 41, 42, 43, 44, 45, 46, 47, 51, 52, 53, 54, 55, 56, 57, 61, 62, 63, 64, 65, 66, 67, 71, 72, 73, 74, 75, 76, 77, 111, 112, 113, 114, 115, 116, 117, 121, 122

Offset: 1

Alois P. Heinz, Jul 25 2012

Alois P. Heinz, Table of n, a(n) for n = 1..10000
R. R. Forslund, A logical alternative to the existing positional number system, Southwest Journal of Pure and Applied Mathematics, Vol. 1, 1995, 27-29.
Eric Weisstein's World of Mathematics, Zerofree
Wikipedia, Bijective numeration

Column k=7 of A214676.

a:= proc(n) local d, l, m; m:= n; l:= NULL;
      while m>0 do d:= irem(m, 7, 'm');
        if d=0 then d:=7; m:= m-1 fi;
        l:= d, l
      od; parse(cat(l))
    end:
seq(a(n), n=1..100);

With[{b = 7}, Flatten@ Table[FromDigits[PadLeft[IntegerDigits[k, b], n] /. k_ :> k + 1], {n, 3}, {k, 0, b^n - 1}] ] (* Michael De Vlieger, Sep 16 2023 *)

A258411 Nonnegative integers n such that in bijective base-2 numeration the number of occurrences of each digit doubles when n is squared.

Original entry on oeis.org

5, 9, 17, 33, 41, 42, 65, 74, 77, 84, 85, 90, 129, 138, 145, 146, 148, 162, 166, 168, 173, 180, 257, 266, 274, 276, 279, 282, 285, 292, 296, 297, 301, 307, 310, 322, 324, 330, 332, 336, 341, 345, 349, 354, 360, 513, 522, 530, 532, 538, 545, 546, 548, 552, 562

Offset: 1

Alois P. Heinz, May 29 2015

			5 = 21_bij2 and 5^2 = 25 = 2121_bij2, 42 = 12122_bij2 and 42^2 = 1764 = 2122211212_bij2.

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Wikipedia, Bijective numeration

Cf. A007931, A214676, A257867, A258410.

p:= proc(n) local d, m, r; m:= n; r:= 0;
      while m>0 do d:= irem(m, 2, 'm');
        if d=0 then d:=2; m:= m-1 fi;
        r:= r+x^d
      od; r
    end:
a:= proc(n) option remember; local k;
      for k from 1+`if`(n=1, 0, a(n-1))
      while p(k)*2<>p(k^2) do od; k
    end:
seq(a(n), n=1..60);

A309908 a(n) is 2^n represented in bijective base-9 numeration.

Original entry on oeis.org

1, 2, 4, 8, 17, 35, 71, 152, 314, 628, 1357, 2725, 5551, 12212, 24424, 48848, 98797, 218715, 438531, 878162, 1867334, 3845668, 7792447, 16694895, 34499911, 69121922, 149243944, 299487988, 619987187, 1342185385, 2684381781, 5478773672, 11968657454, 24148425918

Offset: 0

Alois P. Heinz, Aug 21 2019

Differs from A001357 first at n = 16: a(16) = 98797 < 108807 = A001357(16).

			a(10) =  1357_bij9 =       9*(9*(9*1+3)+5)+7 =  1024 = 2^10.
a(16) = 98797_bij9 = 9*(9*(9*(9*9+8)+7)+9)+7 = 65536 = 2^16.

Alois P. Heinz, Table of n, a(n) for n = 0..1000
R. R. Forslund, A logical alternative to the existing positional number system, Southwest Journal of Pure and Applied Mathematics, Vol. 1, 1995, 27-29.
Eric Weisstein's World of Mathematics, Zerofree
Wikipedia, Bijective numeration

Cf. A000079, A001357, A047855, A052382, A093135, A214676, A325203.

b:= proc(n) local d, l, m; m:= n; l:= "";
      while m>0 do d:= irem(m, 9, 'm');
        if d=0 then d:=9; m:= m-1 fi; l:= d, l
      od; parse(cat(l))
    end:
a:= n-> b(2^n):
seq(a(n), n=0..33);

a(n) = A052382(2^n) = A052382(A000079(n)).

A332395 Expansion of e in bijective base-9 numeration.

Original entry on oeis.org

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

Offset: 1

Alois P. Heinz, Feb 10 2020

The digit set for bijective base-9 numeration is {1, 2, ..., 9}.

The initial 34 digits coincide with those of A004600.

			2.641557364188364258652883785215487391688472363266862162945285212198954...

Alois P. Heinz, Table of n, a(n) for n = 1..10000
R. R. Forslund, A logical alternative to the existing positional number system, Southwest Journal of Pure and Applied Mathematics, Vol. 1, 1995, 27-29.
Eric Weisstein's World of Mathematics, Zerofree
Wikipedia, Bijective numeration

Cf. A001113, A004600, A214676, A332397.

A332397 Expansion of Pi in bijective base-9 numeration.

Original entry on oeis.org

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

Offset: 1

Alois P. Heinz, Feb 10 2020

The digit set for bijective base-9 numeration is {1, 2, ..., 9}.

The initial 9 digits coincide with those of A004608.

			3.124188123974427886451777617299358285165453534626522911263214492838639...

Alois P. Heinz, Table of n, a(n) for n = 1..10000
R. R. Forslund, A logical alternative to the existing positional number system, Southwest Journal of Pure and Applied Mathematics, Vol. 1, 1995, 27-29.
Eric Weisstein's World of Mathematics, Zerofree
Wikipedia, Bijective numeration

Cf. A000796, A004608, A214676, A332395.

cp's OEIS Frontend

A052382 Numbers without 0 in the decimal expansion, colloquial 'zeroless numbers'.

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A214679 A(n,k) = Fibonacci(n) represented in bijective base-k numeration; square array A(n,k), n>=1, k>=1, read by antidiagonals.

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A057436 Contains digits 1 through 6 only.

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A258410 Nonnegative integers with an equal number of occurrences of all digits in bijective base-2 numeration.

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A214678 a(n) = n represented in bijective base-8 numeration.

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A214677 a(n) = n represented in bijective base-7 numeration.

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A258411 Nonnegative integers n such that in bijective base-2 numeration the number of occurrences of each digit doubles when n is squared.

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