cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A284632 Numbers n with digits 2 and 6 only.

Original entry on oeis.org

2, 6, 22, 26, 62, 66, 222, 226, 262, 266, 622, 626, 662, 666, 2222, 2226, 2262, 2266, 2622, 2626, 2662, 2666, 6222, 6226, 6262, 6266, 6622, 6626, 6662, 6666, 22222, 22226, 22262, 22266, 22622, 22626, 22662, 22666, 26222, 26226, 26262, 26266, 26622, 26626
Offset: 1

Views

Author

Jaroslav Krizek, Mar 30 2017

Keywords

Comments

All terms after 2 are composite.

Crossrefs

Cf. A032917.
Numbers n with digits 6 and k only for k = 0..5 and 7..9: A204093 (k = 0), A284293 (k = 1), this sequence (k = 2), A284633 (k = 3), A284634 (k = 4), A256291 (k = 5), A256292 (k = 7), A284635 (k = 8), A284636 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {2, 6}]
  • Mathematica
    Table[Map[FromDigits, Tuples[{2, 6}, {k}]], {k, 5}] // Flatten (* Michael De Vlieger, Mar 30 2017 *)

Formula

a(n) = 2 * A032917(n).

A284634 Numbers with digits 4 and 6 only.

Original entry on oeis.org

4, 6, 44, 46, 64, 66, 444, 446, 464, 466, 644, 646, 664, 666, 4444, 4446, 4464, 4466, 4644, 4646, 4664, 4666, 6444, 6446, 6464, 6466, 6644, 6646, 6664, 6666, 44444, 44446, 44464, 44466, 44644, 44646, 44664, 44666, 46444, 46446, 46464, 46466, 46644, 46646
Offset: 1

Views

Author

Jaroslav Krizek, Apr 02 2017

Keywords

Comments

All terms are even.

Crossrefs

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), this sequence (k = 4), A256291 (k = 5), A256292 (k = 7), A284635 (k = 8), A284636 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {4, 6}]
  • Mathematica
    Table[FromDigits /@ Tuples[{4, 6}, n], {n, 5}] // Flatten (* or *)
Select[Range@ 50000, Total@ Pick[DigitCount@ #, {0, 0, 0, 1, 0, 1, 0, 0, 0, 0}, 0] == 0 &] (* Michael De Vlieger, Apr 02 2017 *)

Formula

a(n) = 2 * A032810(n).

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

Views

Author

Jaroslav Krizek, Apr 02 2017

Keywords

Comments

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

Links

Crossrefs

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).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {6, 9}]
  • Mathematica
    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 *)
  • PARI
    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
  • Python
    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

Formula

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

Views

Author

Jaroslav Krizek, Apr 02 2017

Keywords

Comments

All terms are even.

Crossrefs

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).

Programs

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

Formula

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

A284963 Numbers with digits 3 and 8 only.

Original entry on oeis.org

3, 8, 33, 38, 83, 88, 333, 338, 383, 388, 833, 838, 883, 888, 3333, 3338, 3383, 3388, 3833, 3838, 3883, 3888, 8333, 8338, 8383, 8388, 8833, 8838, 8883, 8888, 33333, 33338, 33383, 33388, 33833, 33838, 33883, 33888, 38333, 38338, 38383, 38388, 38833, 38838
Offset: 1

Views

Author

Jaroslav Krizek, Apr 06 2017

Keywords

Crossrefs

Prime terms are in A020464.
Numbers with digits 3 and k only for k = 0 - 2 and 4 - 9: A169966 (k = 0), A032917 (k = 1), A032810 (k = 2), A032834 (k = 4), A284379 (k = 5), A284633 (k = 6), A143967 (k = 7), this sequence (k = 8), A284964 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {3, 8}]
  • Mathematica
    Table[FromDigits/@Tuples[{3,8},n],{n,5}]//Flatten (* Harvey P. Dale, Mar 23 2021 *)

A284964 Numbers with digits 3 and 9 only.

Original entry on oeis.org

3, 9, 33, 39, 93, 99, 333, 339, 393, 399, 933, 939, 993, 999, 3333, 3339, 3393, 3399, 3933, 3939, 3993, 3999, 9333, 9339, 9393, 9399, 9933, 9939, 9993, 9999, 33333, 33339, 33393, 33399, 33933, 33939, 33993, 33999, 39333, 39339, 39393, 39399, 39933, 39939
Offset: 1

Views

Author

Jaroslav Krizek, Apr 06 2017

Keywords

Comments

All terms > 3 are composite.

Crossrefs

Cf. Numbers with digits 3 and k only for k = 0 - 2 and 4 - 9: A169966 (k = 0), A032917 (k = 1), A032810 (k = 2), A032834 (k = 4), A284379 (k = 5), A284633 (k = 6), A143967 (k = 7), A284963 (k = 8), this sequence (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {3, 9}]
  • Mathematica
    Table[FromDigits/@Tuples[{3,9},n],{n,5}]//Flatten (* Harvey P. Dale, Sep 20 2022 *)

Formula

a(n) = 3 * A032917(n).
Showing 1-6 of 6 results.

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