A007092 -id:A007092 - cp's OEIS frontend

A353114 Base-6 representation of A000422(n).

1, 33, 1253, 32001, 1055253, 22005133, 432020401, 12410423013, 242000505413, 5014143322001, 2210214121042333, 1105325341502010053, 333110135101300035201, 144230053432212010304453, 51542110115212012113433133

Offset: 1

Seiichi Manyama, Apr 24 2022

Cf. A000422, A353110, A353111, A353112, A353113, A353115, A353116, A353117.

Cf. A007092, A353106.

def A(k, n)
  (1..n).map{|i| (1..i).to_a.reverse.join.to_i.to_s(k).to_i}
end
p A(6, 20)

a(n) = A007092(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

A004680 Primes written in base 6.

Original entry on oeis.org

2, 3, 5, 11, 15, 21, 25, 31, 35, 45, 51, 101, 105, 111, 115, 125, 135, 141, 151, 155, 201, 211, 215, 225, 241, 245, 251, 255, 301, 305, 331, 335, 345, 351, 405, 411, 421, 431, 435, 445, 455, 501, 515, 521, 525, 531, 551, 1011, 1015, 1021, 1025, 1035

Offset: 1

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Analogs in other bases: A004676 (base 2), A001363 (base 3), A004678 (base 4), A004679 (base 5), A004681 (base 7), A004682 (base 8), A004683 (base 9), A000040 (base 10), A004684 (base 11).

Cf. A007092.

[Seqint(Intseq(NthPrime(n),6)): n in [1..60]]; // G. C. Greubel, Oct 10 2018

FromDigits/@IntegerDigits[Prime[Range[50]], 6] (* Vincenzo Librandi, Sep 03 2016 *)

a(n)=subst(Pol(digits(prime(n),6)),'x,10) \\ Charles R Greathouse IV, Nov 06 2013

vector(60, n, fromdigits(digits(prime(n), 6))) \\ G. C. Greubel, Oct 10 2018

a(n) = A007092(prime(n)). - Michel Marcus, Sep 03 2016

A037388 Numbers k such that every base-4 digit of k is a base-6 digit of k.

Original entry on oeis.org

1, 2, 3, 15, 38, 55, 63, 73, 85, 91, 117, 119, 121, 127, 170, 231, 236, 243, 255, 256, 257, 264, 276, 288, 289, 290, 291, 292, 293, 294, 306, 324, 325, 326, 327, 336, 341, 343, 348, 349, 350, 351, 362, 375, 381, 383, 408, 409, 410

Offset: 1

Clark Kimberling

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

Cf. A007090, A007092.

Cf. A037387, A037389, A037390, A037391, A037392.

import Data.List ((\\), nub)
a037388 n = a037388_list !! (n-1)
a037388_list = filter f [1..] where
   f x = null $ nub (ds 4 x) \\ nub (ds 6 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[500],SubsetQ[IntegerDigits[#,6],IntegerDigits[#,4]]&] (* Harvey P. Dale, Mar 19 2018 *)

A037393 Numbers k such that every base-5 digit of k is a base-6 digit of k.

Original entry on oeis.org

1, 2, 3, 4, 6, 12, 18, 24, 31, 46, 56, 62, 75, 81, 87, 90, 91, 92, 93, 94, 99, 118, 124, 145, 150, 157, 226, 232, 243, 245, 291, 300, 306, 307, 308, 311, 312, 314, 322, 326, 332, 336, 337, 338, 341, 362, 372, 374, 378, 411, 416, 418

Offset: 1

Clark Kimberling

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

Cf. A007091, A007092.

Cf. A037394, A037395, A037396, A037397.

import Data.List ((\\), nub)
a037393 n = a037393_list !! (n-1)
a037393_list = filter f [1..] where
   f x = null $ nub (ds 5 x) \\ nub (ds 6 x)
   ds b x = if x > 0 then d : ds b x' else []  where (x', d) = divMod x b
-- Reinhard Zumkeller, May 30 2013

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

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 *)

A110604 Numbers n whose base 6 representations, interpreted as base 10 integers, are semiprimes.

Original entry on oeis.org

4, 6, 10, 11, 13, 14, 17, 21, 22, 23, 31, 35, 43, 47, 49, 50, 51, 57, 58, 61, 62, 63, 65, 71, 73, 74, 75, 77, 81, 82, 83, 85, 95, 105, 106, 109, 110, 111, 113, 118, 121, 123, 130, 131, 133, 143, 147, 151, 153, 155, 158, 173, 175, 177, 178, 181, 182, 185, 187, 190, 191

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. A110605 is the equivalent using base 7. A110606 is the equivalent using base 8. A110607 is the equivalent using base 9.

			a(1) = 4 because 4 (base 6) = 4 and 4 (base 10) = 2 * 2, a semiprime (A001358).
a(2) = 6 because 6 (base 6) = 10 and 10 (base 10) = 2 * 5.
a(3) = 10 because 10 (base 6) = 14 and 14 (base 10) = 2 * 7.
a(4) = 11 because 11 (base 6) = 15 and 15 (base 10) = 3 * 5.
a(5) = 13 because 13 (base 6) = 21 and 21 (base 10) = 3 * 7.

Cf. A001358, A007092, A108873, A110602, A110603, A110605, A110606, A110607.

Select[Range[191], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 6]]] == 2 &] (* Ray Chandler, Aug 05 2005 *)
Select[Range[200],PrimeOmega[FromDigits[IntegerDigits[#,6]]]==2&] (* Harvey P. Dale, Oct 02 2011 *)

Corrected and extended by Ray Chandler, Aug 05 2005

A353145 Decimal repunits written in base 6.

Original entry on oeis.org

0, 1, 15, 303, 5051, 123235, 2214223, 35452011, 1034052155, 15005255143, 302130544531, 5034313401115, 123013240420103, 2210234251121451, 35344212440150035, 1032151423443021023, 14535045221530334411, 301223205551110014555

Offset: 0

Seiichi Manyama, Apr 26 2022

Cf. A002275, A291962, A353142, A353143, A353144, A353146, A353147, A353148.

Cf. A003464, A007092.

a(n) = fromdigits(digits((10^n-1)/9, 6));

a(n) = A007092(A002275(n)).

A037399 Numbers k such that every base-6 digit of k is a base-8 digit of k.

Original entry on oeis.org

1, 2, 3, 4, 5, 28, 80, 85, 86, 98, 115, 160, 172, 213, 266, 331, 345, 532, 691, 699, 705, 708, 717, 720, 727, 763, 765, 792, 799, 811, 819, 835, 851, 859, 861, 863, 864, 900, 916, 928, 1036, 1061, 1068, 1085, 1093, 1128, 1129, 1130

Offset: 1

Clark Kimberling

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

Cf. A007092, A007094.

Cf. A037398, A037400, A037401.

import Data.List ((\\), nub)
a037399 n = a037399_list !! (n-1)
a037399_list = filter f [1..] where
   f x = null $ nub (ds 6 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

b68Q[n_]:=Module[{b6=Union[IntegerDigits[n,6]],b8=Union[IntegerDigits[ n,8]]}, And@@Table[ MemberQ[b8,b6[[i]]],{i,Length[b6]}]]; Select[Range[ 1200],b68Q] (* Harvey P. Dale, Mar 24 2012 *)

cp's OEIS Frontend

A353114 Base-6 representation of A000422(n).

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

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A004680 Primes written in base 6.

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A037388 Numbers k such that every base-4 digit of k is a base-6 digit of k.

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A037393 Numbers k such that every base-5 digit of k is a base-6 digit of k.

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A057436 Contains digits 1 through 6 only.

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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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Mathematica

A110604 Numbers n whose base 6 representations, interpreted as base 10 integers, are semiprimes.

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