A204093 -id:A204093 - cp's OEIS frontend

A284633 Numbers n with digits 3 and 6 only.

3, 6, 33, 36, 63, 66, 333, 336, 363, 366, 633, 636, 663, 666, 3333, 3336, 3363, 3366, 3633, 3636, 3663, 3666, 6333, 6336, 6363, 6366, 6633, 6636, 6663, 6666, 33333, 33336, 33363, 33366, 33633, 33636, 33663, 33666, 36333, 36336, 36363, 36366, 36633, 36636

Offset: 1

Jaroslav Krizek, Mar 30 2017

All terms after 3 are composite.

Cf. A007931.

Numbers n with digits 6 and k only for k = 0..5 and 7..9: A204093 (k = 0), A284293 (k = 1), A284632 (k = 2), this sequence (k = 3), A284634 (k = 4), A256291 (k = 5), A256292 (k = 7), A284635 (k = 8), A284636 (k = 9).

[n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {3, 6}]

Table[Map[FromDigits, Tuples[{3, 6}, {k}]], {k, 5}] // Flatten (* Michael De Vlieger, Mar 30 2017 *)

a(n) = 3*A007931(n). - Michel Marcus, Mar 30 2017

A284636 Numbers with digits 6 and 9 only.

Original entry on oeis.org

6, 9, 66, 69, 96, 99, 666, 669, 696, 699, 966, 969, 996, 999, 6666, 6669, 6696, 6699, 6966, 6969, 6996, 6999, 9666, 9669, 9696, 9699, 9966, 9969, 9996, 9999, 66666, 66669, 66696, 66699, 66966, 66969, 66996, 66999, 69666, 69669, 69696, 69699, 69966, 69969

Offset: 1

Jaroslav Krizek, Apr 02 2017

All terms are composite.

All terms are divisible by 3. - Michael S. Branicky, Jun 09 2021

Felix Fröhlich, Table of n, a(n) for n = 1..10000

Cf. A032810.

Numbers n with digits 6 and k only for k = 0 - 5 and 7 - 9: A204093 (k = 0), A284293 (k = 1), A284632 (k = 2), A284633 (k = 3), A284634 (k = 4), A256291 (k = 5), A256292 (k = 7), A284635 (k = 8), this sequence (k = 9).

[n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {6, 9}]

Table[FromDigits /@ Tuples[{6, 9}, n], {n, 5}] // Flatten (* or *)
Select[Range@ 70000, Total@ Pick[DigitCount@ #, {0, 0, 0, 0, 0, 1, 0, 0, 1, 0}, 0] == 0 &] (* Michael De Vlieger, Apr 02 2017 *)

a(n) = {
  my(z, e = logint(n+1,2,&z),
     t1 = 9 * subst(Pol(binary(n+1-z),'x), 'x, 10),
     t2 = 6 * subst(Pol(binary(2*z-2-n),'x), 'x, 10));
  t1+t2;
};
vector(44, n, a(n)) \\ Gheorghe Coserea, Apr 04 2017

def a(n): return int(bin(n+1)[3:].replace('0', '6').replace('1', '9'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, Jun 09 2021

a(n) = 3 * A032810(n).

A284635 Numbers with digits 6 and 8 only.

Original entry on oeis.org

6, 8, 66, 68, 86, 88, 666, 668, 686, 688, 866, 868, 886, 888, 6666, 6668, 6686, 6688, 6866, 6868, 6886, 6888, 8666, 8668, 8686, 8688, 8866, 8868, 8886, 8888, 66666, 66668, 66686, 66688, 66866, 66868, 66886, 66888, 68666, 68668, 68686, 68688, 68866, 68868

Offset: 1

Jaroslav Krizek, Apr 02 2017

All terms are even.

Cf. A032834.

Numbers n with digits 6 and k only for k = 0 - 5 and 7 - 9: A204093 (k = 0), A284293 (k = 1), A284632 (k = 2), A284633 (k = 3), A284634 (k = 4), A256291 (k = 5), A256292 (k = 7), this sequence (k = 8), A284636 (k = 9).

[n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {6, 8}]

Table[FromDigits /@ Tuples[{6, 8}, n], {n, 5}] // Flatten (* or *)
Select[Range@ 70000, Total@ Pick[DigitCount@ #, {0, 0, 0, 0, 0, 1, 0, 1, 0, 0}, 0] == 0 &] (* Michael De Vlieger, Apr 02 2017 *)

def a(n): return int(bin(n+1)[3:].replace('0', '6').replace('1', '8'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, Jun 08 2021

a(n) = 2 * A032834(n).

A078245 Smallest multiple of n using only digits 0 and 6.

Original entry on oeis.org

6, 6, 6, 60, 60, 6, 6006, 600, 666, 60, 66, 60, 6006, 6006, 60, 6000, 66606, 666, 66006, 60, 6006, 66, 660606, 600, 600, 6006, 666666666, 60060, 6606606, 60, 666066, 60000, 66, 66606, 60060, 6660, 666, 66006, 6006, 600, 66666, 6006, 6606606, 660, 6660, 660606

Offset: 1

Amarnath Murthy, Nov 23 2002

a(n) = min{A204093(k): k > 0 and A204093(k) mod n = 0}. [Reinhard Zumkeller, Jan 10 2012]

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Reinhard Zumkeller)

Cf. A004290, A078241-A078248, A079339, A096681-A096688.

a078245 n = head [x | x <- tail a204093_list, mod x n == 0]
-- Reinhard Zumkeller, Jan 10 2012

With[{c=Rest[FromDigits/@Tuples[{0,6},10]]},Table[SelectFirst[c,Divisible[ #,n]&],{n,50}]] (* The program uses the SelectFirst function from Mathematica version 10 *) (* Harvey P. Dale, Apr 15 2015 *)

def A204093(n): return int(bin(n)[2:].replace('1', '6'))
def a(n):
    k = 1
    while A204093(k)%n: k += 1
    return A204093(k)
print([a(n) for n in range(1, 47)]) # Michael S. Branicky, Jun 06 2021

More terms from Ray Chandler, Jul 12 2004

cp's OEIS Frontend

A284633 Numbers n with digits 3 and 6 only.

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A284636 Numbers with digits 6 and 9 only.

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A284635 Numbers with digits 6 and 8 only.

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A078245 Smallest multiple of n using only digits 0 and 6.

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