A007094 -id:A007094 - cp's OEIS frontend

A353116 Base-8 representation of A000422(n).

1, 25, 501, 10341, 152061, 2375761, 35145661, 516277661, 7267464261, 121672446261, 20125401442261, 3342313131342261, 564731226736442261, 116343242472501442261, 20325073566675147442261, 3327107422474572347442261

Offset: 1

Seiichi Manyama, Apr 24 2022

Cf. A000422, A353110, A353111, A353112, A353113, A353114, A353115, A353117.

Cf. A007094, A097583.

def A(k, n)
  (1..n).map{|i| (1..i).to_a.reverse.join.to_i.to_s(k).to_i}
end
p A(8, 20)

a(n) = A007094(A000422(n)).

A004053 For m=2,3,..., write m in bases 2,3,..,m.

Original entry on oeis.org

10, 11, 10, 100, 11, 10, 101, 12, 11, 10, 110, 20, 12, 11, 10, 111, 21, 13, 12, 11, 10, 1000, 22, 20, 13, 12, 11, 10, 1001, 100, 21, 14, 13, 12, 11, 10, 1010, 101, 22, 20, 14, 13, 12, 11, 10, 1011, 102, 23, 21, 15, 14, 13, 12, 11, 10, 1100, 110, 30, 22, 20, 15, 14, 13, 12, 11, 10

Offset: 2

Johan Boye (johbo(AT)ida.liu.se)

			Triangle begins:
    10;
    11,  10;
   100,  11, 10;
   101,  12, 11, 10;
   110,  20, 12, 11, 10;
   111,  21, 13, 12, 11, 10;
  1000,  22, 20, 13, 12, 11, 10;
  1001, 100, 21, 14, 13, 12, 11, 10;
  ...

Alois P. Heinz, Rows n = 2..20, flattened (row 21 would require digits > 9)

Cf. A007088, A007090, A007091, A007092, A007093, A007094, A007095.

FromDigits/@Flatten[Table[IntegerDigits[m,b],{m,2,20},{b,2,m}],1] (* Harvey P. Dale, Dec 01 2024 *)

T(n, k) = fromdigits(digits(n, k), 10);
tabl(nn) = for (n=2, nn, for (b=2, n, print1(T(n, b), ", "))); \\ Michel Marcus, Aug 30 2019

A037390 Numbers k such that every base-4 digit of k is a base-8 digit of k.

Original entry on oeis.org

1, 2, 3, 10, 42, 64, 65, 66, 67, 68, 69, 80, 85, 86, 90, 93, 95, 106, 128, 129, 130, 131, 136, 153, 160, 168, 169, 170, 171, 187, 192, 193, 194, 195, 234, 240, 250, 255, 257, 321, 514, 522, 528, 529, 530, 531, 532, 533, 534, 538

Offset: 1

Clark Kimberling

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

Cf. A007090, A007094.

Cf. A037387, A037388, A037389, A037391, A037392.

import Data.List ((\\), nub)
a037390 n = a037390_list !! (n-1)
a037390_list = filter f [1..] where
   f x = null $ nub (ds 4 x) \\ nub (ds 8 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

A037395 Numbers k such that every base-5 digit of k is a base-8 digit of k.

Original entry on oeis.org

1, 2, 3, 4, 83, 91, 93, 99, 124, 136, 161, 200, 206, 272, 314, 467, 524, 532, 540, 545, 546, 549, 609, 643, 656, 672, 680, 705, 706, 708, 770, 771, 774, 775, 776, 781, 784, 786, 787, 789, 793, 794, 796, 798, 799, 843, 871, 906

Offset: 1

Clark Kimberling

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

Cf. A007091, A007094.

Cf. A037393, A037394, A037396, A037397.

import Data.List ((\\), nub)
a037395 n = a037395_list !! (n-1)
a037395_list = filter f [1..] where
   f x = null $ nub (ds 5 x) \\ nub (ds 8 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

Select[Range[1000],SubsetQ[IntegerDigits[#,8],IntegerDigits[#,5]]&] (* Harvey P. Dale, Oct 13 2015 *)

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

Original entry on oeis.org

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 *)

A102681 Number of digits >= 8 in decimal representation of n.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Feb 03 2005

a(n) = 0 iff n is in A007094 (numbers in base 8). - Bernard Schott, Feb 18 2023

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Cf. A007094, A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564. Partial sums see A102682.

Cf. A000120, A000788, A023416, A059015 (for base 2).

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]>=8 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(p(n),n=0..120); # Emeric Deutsch, Feb 23 2005

From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = Sum_{j=1..m+1} (floor(n/10^j + 1/5) - floor(n/10^j)), where m = floor(log_10(n)).
G.f.: g(x) = (1/(1-x))*Sum_{j>=0} (x^(8*10^j) - x^(10*10^j))/(1 - x^10^(j+1)). (End)

More terms from Emeric Deutsch, Feb 23 2005

A110606 Numbers n whose base 8 representations, interpreted as base 10 integers, are semiprimes.

Original entry on oeis.org

4, 6, 8, 12, 13, 17, 18, 21, 22, 27, 28, 29, 38, 41, 45, 47, 50, 53, 60, 63, 70, 73, 77, 81, 82, 83, 91, 92, 97, 98, 99, 101, 102, 109, 113, 118, 127, 129, 130, 131, 133, 134, 139, 140, 141, 143, 145, 150, 157, 159, 167, 171, 172, 178, 181, 183, 188, 193, 194, 195

Offset: 1

Jonathan Vos Post, Jul 30 2005

A108873 is the equivalent using base 3. A110602 is the equivalent using base 4. A110603 is the equivalent using base 5. A110604 is the equivalent using base 6. A110605 is the equivalent using base 7. A110607 is the equivalent using base 9.

			a(1) = 4 because 4 (base 8) = 4 (base 10) = 2 * 2, a semiprime (A001358).
a(2) = 6 because 6 (base 8) = 6 (base 10) = 2 * 3.
a(3) = 8 because 8 (base 8) = 10 and 10 (base 10) = 2 * 5.
a(4) = 12 because 12 (base 8) = 14 and 14 (base 10) = 2 * 7.
a(5) = 13 because 13 (base 8) = 15 and 15 (base 10) = 3 * 5.

Cf. A001358, A007094, A108873, A110602, A110603, A110604, A110605, A110607.

Select[Range[195], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 8]]] == 2 &] (* Ray Chandler, Aug 05 2005 *)

Extended by Ray Chandler, Aug 05 2005

A353147 Decimal repunits written in base 8.

Original entry on oeis.org

0, 1, 13, 157, 2127, 25547, 331007, 4172107, 52305307, 647665707, 10216432707, 122621414707, 1473657200707, 20126330410707, 241540165130707, 3120702223570707, 37450626705270707, 473627744665470707, 6125757360430070707, 75533532545361070707

Offset: 0

Seiichi Manyama, Apr 26 2022

Cf. A002275, A291962, A353142, A353143, A353144, A353145, A353146, A353148.

Cf. A007094, A023001.

a(n) = fromdigits(digits((10^n-1)/9, 8));

def a(n): return 0 if n == 0 else int(oct(int("1"*n))[2:])
print([a(n) for n in range(13)]) # Michael S. Branicky, Apr 26 2022

a(n) = A007094(A002275(n)).

A000433 n written in base where place values are positive cubes.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 100, 101, 102, 103, 104, 105, 106, 107, 110, 111, 112, 113, 114, 115, 116, 117, 120, 121, 122, 123, 124, 125, 126, 127, 130, 131, 132, 200, 201, 202, 203

Offset: 0

R. Muller

Let [d1, d2, d3, ...] be the decimal expansion of the n-th term, then dk is the number of times that the greedy algorithm subtracts the cube k^3 with input n. - Joerg Arndt, Nov 21 2014
For n > 1: A048766(n) = number of digits of a(n); A190311(n) = number of nonzero digits of a(n); A055401(n) = sum of digits of a(n). - Reinhard Zumkeller, May 08 2011
First differs from numbers written in base 8 (A007094) at a(27) = 100, whereas A007094(27) = 33. - Alonso del Arte, Nov 27 2014
The rightmost (least significant) digit never exceeds 7, the second digit from the right never exceeds 3, the third digit never exceeds 2, and the rest are just 0's and 1's. - Ivan Neretin, Sep 03 2015

			a(26) = 32 because 26 = 3 * 2^3 + 2 * 1^3.
a(27) = 100 because 27 = 3^3 + 0 * 2^3 + 0 * 1^3.
a(28) = 101 because 28 = 3^3 + 0 * 2^3 + 1 * 1^3.

Florentin Smarandache, "Properties of the Numbers", University of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ.

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

Cf. A000578, A007961.

import Data.Char (intToDigit)
a000433 0 = 0
a000433 n = read $ map intToDigit $
  t n $ reverse $ takeWhile (<= n) $ tail a000578_list where
      t _ []          = []
      t m (x:xs)
          | x > m     = 0 : t m xs
          | otherwise = (fromInteger m') : t r xs where (m',r) = divMod m x
-- Reinhard Zumkeller, May 08 2011

A036285 Sequence A036284 written in octal.

Original entry on oeis.org

6, 30, 2640, 25664300, 2503026643656400, 25315703023056664357316564563000, 2527515731736303020414563050266643413731571505656462723056364000, 25246137277231573150136315064303020122720413505630571426364566664342075141145731573675057360256564674414627536305631724050230000

Offset: 0

Antti Karttunen, Nov 01 1998

A. Karttunen, Table of n, a(n) for n = 0..9
A. Karttunen, C program for computing this sequence

Cf. A136381, A136383, A136385.

a(n) = A007094(A036284(n)).

Entry revised Dec 29 2007

cp's OEIS Frontend

A353116 Base-8 representation of A000422(n).

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A004053 For m=2,3,..., write m in bases 2,3,..,m.

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A037390 Numbers k such that every base-4 digit of k is a base-8 digit of k.

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A037395 Numbers k such that every base-5 digit of k is a base-8 digit of k.

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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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A102681 Number of digits >= 8 in decimal representation of n.

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A110606 Numbers n whose base 8 representations, interpreted as base 10 integers, are semiprimes.

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Mathematica

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A353147 Decimal repunits written in base 8.

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A000433 n written in base where place values are positive cubes.

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