A007095 -id:A007095 - cp's OEIS frontend

A063432 Triangle read by rows in which k-th entry in row n is representation of n in base k, for 1 <= k <= n.

1, 11, 10, 111, 11, 10, 1111, 100, 11, 10, 11111, 101, 12, 11, 10, 111111, 110, 20, 12, 11, 10, 1111111, 111, 21, 13, 12, 11, 10, 11111111, 1000, 22, 20, 13, 12, 11, 10, 111111111, 1001, 100, 21, 14, 13, 12, 11, 10, 1111111111, 1010, 101, 22, 20, 14, 13

Offset: 1

Henry Bottomley, Jul 20 2001

Representation of n in base 1 is defined to be a concatenation of n 1's.
It is difficult to write twenty-one in base 11 using decimal digits.
Representation in bases greater than 10 are written in base 10. This is really nasty! - N. J. A. Sloane, Dec 06 2002

			Rows start (1), (11, 10), (111, 11, 10), (1111, 100, 11, 10), etc.

Cf. A063431.
Rows are effectively the reverse of A001731, A001732, A001733, A001734, A001735, A001736, A008707, A008708, A008709, A008710, A008711, A008712, A008713, A008714, A008715, A008716, A008717, etc.
Columns are truncated versions of A000042, A007088, A007089, A007090, A007091, A007092, A007093, A007094, A007095, A000027 and perhaps A055649, etc.
Without the 1st column becomes A004053.

f[n_] := Flatten[ Append[ {FromDigits[ Table[1, {n}]] }, Table[ FromDigits[ IntegerDigits[n, i]], {i, 2, n}]]]; Flatten[ Table[ f[n], {n, 1, 10}]] (* Robert G. Wilson v *)

A353148 Decimal repunits written in base 9.

Original entry on oeis.org

0, 1, 12, 133, 1464, 16215, 178366, 2073137, 22814518, 252060710, 2772667811, 31610457022, 347715137243, 3835866520674, 43305642727525, 476363171113776, 5351104882252647, 58862154814780228, 658583714063682520, 7355531854711617721, 82021851512827806032

Offset: 0

Seiichi Manyama, Apr 26 2022

Cf. A002275, A291962, A353142, A353143, A353144, A353145, A353146, A353147.

Cf. A002452, A007095, A055479.

a(n) = fromdigits(digits((10^n-1)/9, 9));

a(n) = A007095(A002275(n)).

a(n) = (A055479(n) - 1)/10. - Hugo Pfoertner, Apr 26 2022

A031954 Numbers with exactly two distinct base-9 digits.

Original entry on oeis.org

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, 90, 92, 93, 94, 95, 96, 97, 98, 100, 101, 109, 111

Offset: 1

Clark Kimberling

Cf. A007095.

isA031954 := proc(n)
    local dgs,p,s ;
    dgs := convert(convert(n,base,9),set) ;
    if nops(dgs) = 2 then
        true ;
    else
        false ;
    end if ;
end proc:
A031954 := proc(n)
    option remember ;
    if n =1 then
        9 ;
    else
        for a from procname(n-1)+1 do
            if isA031954(a) then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A031954(n),n=1..80) ; # R. J. Mathar, Jan 24 2023

a(n)=n+8+(n+7)\9 \\ Charles R Greathouse IV, Mar 10 2021

A033035 Numbers such that all base 9 digits are odd.

Original entry on oeis.org

1, 3, 5, 7, 10, 12, 14, 16, 28, 30, 32, 34, 46, 48, 50, 52, 64, 66, 68, 70, 91, 93, 95, 97, 109, 111, 113, 115, 127, 129, 131, 133, 145, 147, 149, 151, 253, 255, 257, 259, 271, 273, 275, 277, 289, 291, 293, 295, 307, 309, 311, 313, 415

Offset: 1

Clark Kimberling

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

Cf. A007095 (numbers in base 9).

f:= proc(n) option remember; local m;
  m:= floor((n-1)/4);
  9*procname(m) + 2*n - 8*m - 1
end proc:
f(0):= 0:
map(f, [$1..100]); # Robert Israel, Jan 23 2019

Select[Range[500],AllTrue[IntegerDigits[#,9],OddQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 14 2015 *)
Flatten[Table[FromDigits[#,9]&/@Tuples[Range[1,7,2],n],{n,3}]] (* Harvey P. Dale, Jun 13 2020 *)

a(4n+j) = 9*a(n)+2*j-1 for j=1..4. - Robert Israel, Jan 23 2019

A353107 Base-9 representation of A007908(n).

Original entry on oeis.org

1, 13, 146, 1621, 17836, 207313, 2281451, 25206070, 277266780, 34771513601, 4330564256733, 535110486286816, 65858371163036861, 8202185121837583406, 1113465620754570813253, 134741562223525280514741, 16425841240157671153405780

Offset: 1

Seiichi Manyama, Apr 23 2022

Seiichi Manyama, Table of n, a(n) for n = 1..354

Cf. A007908, A050926, A097580, A097582, A097583, A353104, A353105, A353106.

Cf. A007095.

def A(k, n)
  (1..n).map{|i| (1..i).to_a.join.to_i.to_s(k).to_i}
end
p A(9, 20)

a(n) = A007095(A007908(n)).

A382418 Numbers with at least one zero in their base-9 representation.

Original entry on oeis.org

0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 99, 108, 117, 126, 135, 144, 153, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 180, 189, 198, 207, 216, 225, 234, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 261, 270, 279, 288, 297

Offset: 1

Paolo Xausa, Mar 25 2025

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. analogous sequences in other bases: A062289 (base 2), A081605 (base 3), A196032 (base 4), A382415 (base 5), A382416 (base 6), A382413 (base 7), A382417 (base 8), A011540 (base 10).

Cf. A007095, A043453, A255808 (complement).

Select[Range[0, 300], DigitCount[#, 9, 0] > 0 &]

A004683 Primes written in base 9.

Original entry on oeis.org

2, 3, 5, 7, 12, 14, 18, 21, 25, 32, 34, 41, 45, 47, 52, 58, 65, 67, 74, 78, 81, 87, 102, 108, 117, 122, 124, 128, 131, 135, 151, 155, 162, 164, 175, 177, 184, 201, 205, 212, 218, 221, 232, 234, 238, 241, 254, 267

Offset: 1

N. J. A. Sloane

Zak Seidov, Table of n, a(n) for n = 1..1000

Subsequence of A007095.

[Seqint(Intseq(NthPrime(n),9)): n in [1..50]]; // G. C. Greubel, Oct 09 2018

Table[FromDigits[IntegerDigits[Prime[n], 9]], {n, 100}] (* Zak Seidov, Apr 25 2016 *)

a(n)=subst(Pol(digits(prime(n),9)),'x,10) \\ Charles R Greathouse IV, Nov 06 2013

vector(50, n, fromdigits(digits(prime(n), 9))) \\ G. C. Greubel, Oct 09 2018

A032864 Numbers whose base-9 representation Sum_{i=0..m} d(i)*9^i has d(m) > d(m-1) < d(m-2) > ...

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 19, 27, 28, 29, 36, 37, 38, 39, 45, 46, 47, 48, 49, 54, 55, 56, 57, 58, 59, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 163, 164, 165, 166, 167, 168, 169, 170, 173

Offset: 1

Clark Kimberling

Cf. A007095.
Different from A032888.
Cf. A032858..A032865 for bases 3..10.
Cf. A306106..A306111 and A297147 for bases 3..9 and 10.

a(1)=0 inserted by Georg Fischer, Dec 18 2020

A037400 Numbers k such that every base-6 digit of k is a base-9 digit of k.

Original entry on oeis.org

1, 2, 3, 4, 5, 21, 104, 108, 115, 129, 194, 212, 215, 252, 259, 271, 280, 352, 370, 388, 417, 504, 651, 756, 757, 758, 759, 760, 761, 762, 763, 777, 913, 922, 928, 932, 949, 976, 994, 1008, 1015, 1030, 1076, 1137, 1147, 1151, 1152

Offset: 1

Clark Kimberling

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

Cf. A007092, A007095.

Cf. A037398, A037399, A037401.

import Data.List ((\\), nub)
a037400 n = a037400_list !! (n-1)
a037400_list = filter f [1..] where
   f x = null $ nub (ds 6 x) \\ nub (ds 9 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

A037403 Numbers k such that every base-7 digit of k is a base-9 digit of k.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 31, 99, 106, 107, 195, 198, 248, 257, 284, 297, 321, 498, 514, 749, 750, 751, 758, 767, 785, 936, 939, 940, 943, 950, 968, 996, 1028, 1086, 1088, 1110, 1163, 1200, 1218, 1254, 1453, 1471, 1498, 1500, 1502, 1507

Offset: 1

Clark Kimberling

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

Cf. A007093, A007095.

Cf. A037402, A037404.

import Data.List ((\\), nub)
a037403 n = a037403_list !! (n-1)
a037403_list = filter f [1..] where
   f x = null $ nub (ds 7 x) \\ nub (ds 9 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

cp's OEIS Frontend

A063432 Triangle read by rows in which k-th entry in row n is representation of n in base k, for 1 <= k <= n.

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Mathematica

A353148 Decimal repunits written in base 9.

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PARI

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A031954 Numbers with exactly two distinct base-9 digits.

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Maple

PARI

A033035 Numbers such that all base 9 digits are odd.

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Maple

Mathematica

Formula

A353107 Base-9 representation of A007908(n).

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Ruby

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A382418 Numbers with at least one zero in their base-9 representation.

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Mathematica

A004683 Primes written in base 9.

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Magma

Mathematica

PARI

PARI

A032864 Numbers whose base-9 representation Sum_{i=0..m} d(i)*9^i has d(m) > d(m-1) < d(m-2) > ...

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Extensions

A037400 Numbers k such that every base-6 digit of k is a base-9 digit of k.

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Haskell

A037403 Numbers k such that every base-7 digit of k is a base-9 digit of k.

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