A007091 -id:A007091 - cp's OEIS frontend

A037394 Numbers k such that every base-5 digit of k is a base-7 digit of k.

1, 2, 3, 4, 17, 51, 66, 102, 109, 123, 156, 158, 162, 206, 218, 312, 317, 324, 361, 381, 416, 418, 423, 458, 462, 463, 466, 467, 468, 472, 494, 518, 545, 546, 549, 556, 557, 559, 562, 584, 606, 619, 621, 630, 640, 651, 658, 687

Offset: 1

Clark Kimberling

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

Cf. A007091, A007093.

Cf. A037393, A037395, A037396, A037397.

import Data.List ((\\), nub)
a037394 n = a037394_list !! (n-1)
a037394_list = filter f [1..] where
   f x = null $ nub (ds 5 x) \\ nub (ds 7 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[700],SubsetQ[IntegerDigits[#,7],IntegerDigits[#,5]]&] (* Harvey P. Dale, Sep 29 2017 *)

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 *)

A037454 a(n) = Sum_{i=0..m} d(i)6^i, where Sum_{i=0..m} d(i)3^i is the base 3 representation of n.

Original entry on oeis.org

0, 1, 2, 6, 7, 8, 12, 13, 14, 36, 37, 38, 42, 43, 44, 48, 49, 50, 72, 73, 74, 78, 79, 80, 84, 85, 86, 216, 217, 218, 222, 223, 224, 228, 229, 230, 252, 253, 254, 258, 259, 260, 264, 265, 266, 288, 289, 290, 294, 295, 296, 300, 301, 302, 432, 433, 434, 438

Offset: 0

Clark Kimberling

Clark Kimberling, Table of n, a(n) for n = 0..1000

Cf. A037462, A007091, A102491.

function a(n)
    m, r, b = n, 0, 1
    while m > 0
        m, q = divrem(m, 3)
        r += b * q
        b *= 6
    end
r end; [a(n) for n in 0:57] |> println # Peter Luschny, Jan 03 2021

seq(n + (1/2)*add(6^k*floor(n/3^k), k = 1..floor(ln(n)/ln(3))), n = 1..100); # Peter Bala, Dec 01 2016

t = Table[FromDigits[RealDigits[n, 3], 6], {n, 0, 100}]
(* Clark Kimberling, Aug 03 2012 *)

From Peter Bala, Dec 01 2016: (Start)
a(n) = n + 1/2*Sum_{k >= 1} 6^k*floor(n/3^k). Cf. A037462, A007091 and A102491.
a(0) = 0; a(n) = 6*a(n/3) if n == 0 (mod 3) else a(n) = a(n-1) + 1. (End)

Offset changed to 0 by Clark Kimberling, Aug 03 2012

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 *)

A277543 a(n) = n/5^m mod 5, where 5^m is the greatest power of 5 that divides n.

Original entry on oeis.org

1, 2, 3, 4, 1, 1, 2, 3, 4, 2, 1, 2, 3, 4, 3, 1, 2, 3, 4, 4, 1, 2, 3, 4, 1, 1, 2, 3, 4, 1, 1, 2, 3, 4, 2, 1, 2, 3, 4, 3, 1, 2, 3, 4, 4, 1, 2, 3, 4, 2, 1, 2, 3, 4, 1, 1, 2, 3, 4, 2, 1, 2, 3, 4, 3, 1, 2, 3, 4, 4, 1, 2, 3, 4, 3, 1, 2, 3, 4, 1, 1, 2, 3, 4, 2, 1

Offset: 1

Clark Kimberling, Oct 19 2016

a(n) is the rightmost nonzero digit in the base 5 expansion of n (A007091).

			a(20) = (20/5 mod 5) = 4.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A007091, A010874, A132739.

Cf. A277550, A277551, A277555, A277548 (positions of 1, 2, 3 and 4 in this sequence).

Table[Mod[n/5^IntegerExponent[n, 5], 5], {n, 1, 160}]

a(n) = n/5^valuation(n, 5) % 5; \\ Michel Marcus, Oct 20 2016

a(n) = A132739(n) mod 5 = A010874(A132739(n)). - Michel Marcus, Oct 20 2016

A353144 Decimal repunits written in base 5.

Original entry on oeis.org

0, 1, 21, 421, 13421, 323421, 12023421, 241023421, 10321023421, 211421023421, 4233421023421, 140223421023421, 3310023421023421, 121201023421023421, 2424021023421023421, 104030421023421023421, 2131113421023421023421, 43122323421023421023421, 1413002023421023421023421

Offset: 0

Seiichi Manyama, Apr 26 2022

Cf. A002275, A291962, A353142, A353143, A353145, A353146, A353147, A353148.

Cf. A003463, A007091.

a(n) = fromdigits(digits((10^n-1)/9, 5));

a(n) = A007091(A002275(n)).

A004679 Primes written in base 5.

Original entry on oeis.org

2, 3, 10, 12, 21, 23, 32, 34, 43, 104, 111, 122, 131, 133, 142, 203, 214, 221, 232, 241, 243, 304, 313, 324, 342, 401, 403, 412, 414, 423, 1002, 1011, 1022, 1024, 1044, 1101, 1112, 1123, 1132, 1143, 1204, 1211, 1231, 1233, 1242, 1244, 1321, 1343, 1402, 1404, 1413, 1424, 1431

Offset: 1

N. J. A. Sloane

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

Cf. similar sequences listed in A004680.

Cf. A000040, A007091.

[Seqint(Intseq(NthPrime(n), 5)): n in [1..60]]; // G. C. Greubel, Oct 12 2018

FromDigits/@IntegerDigits[Prime[Range[50]],5] (* Harvey P. Dale, Dec 09 2010 *)

a(n)=subst(Pol(digits(prime(n),5)),'x,10) \\ Charles R Greathouse IV, Nov 06 2013

a(n) = A007091(A000040(n)). - Michel Marcus, Sep 03 2016

A309956 Product of digits of (n written in base 5).

Original entry on oeis.org

0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 2, 4, 6, 8, 0, 3, 6, 9, 12, 0, 4, 8, 12, 16, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 0, 2, 4, 6, 8, 0, 3, 6, 9, 12, 0, 4, 8, 12, 16, 0, 0, 0, 0, 0, 0, 2, 4, 6, 8, 0, 4, 8, 12, 16, 0, 6, 12, 18, 24, 0, 8, 16, 24, 32, 0, 0, 0, 0, 0, 0, 3, 6, 9, 12, 0, 6, 12, 18, 24, 0, 9, 18, 27, 36, 0, 12, 24, 36, 48, 0

Offset: 0

Ilya Gutkovskiy, Aug 24 2019

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Cf. A007091, A007954, A053824.

[0] cat [&*Intseq(n,5):n in [1..100]]; // Marius A. Burtea, Aug 25 2019

Table[Times @@ IntegerDigits[n, 5], {n, 0, 100}]

a(n) = my(d = if (n, digits(n,5), [0])); vecprod(d); \\ Michel Marcus, Aug 25 2019

G.f. A(x) satisfies: A(x) = x * (1 + 2*x + 3*x^2 + 4*x^3) * (1 + A(x^5)).

A353105 Base-5 representation of A007908(n).

Original entry on oeis.org

1, 22, 443, 14414, 343340, 12422311, 304001232, 11130030203, 223101104124, 200240443211120, 130211343340003021, 112140204001002213422, 100421133100401442024323, 40324014240311242321340224, 31241112311230113034201201130

Offset: 1

Seiichi Manyama, Apr 23 2022

Seiichi Manyama, Table of n, a(n) for n = 1..269

Cf. A007908, A050926, A097580, A097582, A097583, A353104, A353106, A353107.

Cf. A007091.

def A(k, n)
  (1..n).map{|i| (1..i).to_a.join.to_i.to_s(k).to_i}
end
p A(5, 20)

a(n) = A007091(A007908(n)).

A382415 Numbers with at least one zero in their base-5 representation.

Original entry on oeis.org

0, 5, 10, 15, 20, 25, 26, 27, 28, 29, 30, 35, 40, 45, 50, 51, 52, 53, 54, 55, 60, 65, 70, 75, 76, 77, 78, 79, 80, 85, 90, 95, 100, 101, 102, 103, 104, 105, 110, 115, 120, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145

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), A382416 (base 6), A382413 (base 7), A382417 (base 8), A382418 (base 9), A011540 (base 10).

Cf. A007091, A023721 (complement), A023722.

Select[Range[0, 150], DigitCount[#, 5, 0] > 0 &]

cp's OEIS Frontend

A037394 Numbers k such that every base-5 digit of k is a base-7 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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A037454 a(n) = Sum_{i=0..m} d(i)*6^i, where Sum_{i=0..m} d(i)*3^i is the base 3 representation of n.

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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

A277543 a(n) = n/5^m mod 5, where 5^m is the greatest power of 5 that divides n.

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Mathematica

PARI

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A353144 Decimal repunits written in base 5.

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PARI

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A004679 Primes written in base 5.

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Magma

Mathematica

PARI

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A309956 Product of digits of (n written in base 5).

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Magma

Mathematica

A037454 a(n) = Sum_{i=0..m} d(i)6^i, where Sum_{i=0..m} d(i)3^i is the base 3 representation of n.