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 1-9 of 9 results.

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).

A284633 Numbers n with digits 3 and 6 only.

Original entry on oeis.org

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

Views

Author

Jaroslav Krizek, Mar 30 2017

Keywords

Comments

All terms after 3 are composite.

Crossrefs

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).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {3, 6}]
  • Mathematica
    Table[Map[FromDigits, Tuples[{3, 6}, {k}]], {k, 5}] // Flatten (* Michael De Vlieger, Mar 30 2017 *)

Formula

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

A284920 Numbers with digits 2 and 4 only.

Original entry on oeis.org

2, 4, 22, 24, 42, 44, 222, 224, 242, 244, 422, 424, 442, 444, 2222, 2224, 2242, 2244, 2422, 2424, 2442, 2444, 4222, 4224, 4242, 4244, 4422, 4424, 4442, 4444, 22222, 22224, 22242, 22244, 22422, 22424, 22442, 22444, 24222, 24224, 24242, 24244, 24422, 24424
Offset: 1

Views

Author

Jaroslav Krizek, Apr 05 2017

Keywords

Comments

All terms are even.

Crossrefs

Cf. Numbers with digits 2 and k only for k = 0 - 1 and 3 - 9: A169965 (k = 0), A007931 (k = 1), A032810 (k = 3), this sequence (k = 4), A072961 (k = 5), A284632 (k = 6), A284921 (k = 7), A284922 (k = 8), A284923 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {2, 4}]
  • Mathematica
    Flatten@ Array[FromDigits /@ Tuples[{2, 4}, #] &, 5] (* Michael De Vlieger, Apr 06 2017 *)

Formula

a(n) = 2 * A007931(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).

A284921 Numbers with digits 2 and 7 only.

Original entry on oeis.org

2, 7, 22, 27, 72, 77, 222, 227, 272, 277, 722, 727, 772, 777, 2222, 2227, 2272, 2277, 2722, 2727, 2772, 2777, 7222, 7227, 7272, 7277, 7722, 7727, 7772, 7777, 22222, 22227, 22272, 22277, 22722, 22727, 22772, 22777, 27222, 27227, 27272, 27277, 27722, 27727
Offset: 1

Views

Author

Jaroslav Krizek, Apr 05 2017

Keywords

Comments

Prime terms are in A020459.

Crossrefs

Cf. Numbers with digits 2 and k only for k = 0 - 1 and 3 - 9: A169965 (k = 0), A007931 (k = 1), A032810 (k = 3), A284920 (k = 4), A072961 (k = 5), A284632 (k = 6), this sequence (k = 7), A284922 (k = 8), A284923 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {2, 7}]
  • Mathematica
    Flatten@ Array[FromDigits /@ Tuples[{2, 7}, #] &, 5] (* Michael De Vlieger, Apr 06 2017 *)

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).

A284922 Numbers with digits 2 and 8 only.

Original entry on oeis.org

2, 8, 22, 28, 82, 88, 222, 228, 282, 288, 822, 828, 882, 888, 2222, 2228, 2282, 2288, 2822, 2828, 2882, 2888, 8222, 8228, 8282, 8288, 8822, 8828, 8882, 8888, 22222, 22228, 22282, 22288, 22822, 22828, 22882, 22888, 28222, 28228, 28282, 28288, 28822, 28828
Offset: 1

Views

Author

Jaroslav Krizek, Apr 05 2017

Keywords

Comments

All terms are even.

Crossrefs

Cf. Numbers with digits 2 and k only for k = 0 - 1 and 3 - 9: A169965 (k = 0), A007931 (k = 1), A032810 (k = 3), A284920 (k = 4), A072961 (k = 5), A284632 (k = 6), A284921 (k = 7), this sequence (k = 8), A284923 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {2, 8}]
  • Mathematica
    Flatten@ Array[FromDigits /@ Tuples[{2, 8}, #] &, 5] (* Michael De Vlieger, Apr 06 2017 *)

Formula

a(n) = 2 * A032822(n).

A284923 Numbers with digits 2 and 9 only.

Original entry on oeis.org

2, 9, 22, 29, 92, 99, 222, 229, 292, 299, 922, 929, 992, 999, 2222, 2229, 2292, 2299, 2922, 2929, 2992, 2999, 9222, 9229, 9292, 9299, 9922, 9929, 9992, 9999, 22222, 22229, 22292, 22299, 22922, 22929, 22992, 22999, 29222, 29229, 29292, 29299, 29922, 29929
Offset: 1

Views

Author

Jaroslav Krizek, Apr 06 2017

Keywords

Crossrefs

Prime terms are in A020460.
Numbers with digits 2 and k only for k = 0 - 1 and 3 - 9: A169965 (k = 0), A007931 (k = 1), A032810 (k = 3), A284920 (k = 4), A072961 (k = 5), A284632 (k = 6), A284921 (k = 7), A284922 (k = 8), this sequence (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {2, 9}]
  • Mathematica
    Select[Range[30000],SubsetQ[{2,9},Sort[DeleteDuplicates[IntegerDigits[#]]]] &] (* Stefano Spezia, Aug 06 2025 *)

A343823 Numbers k > 10 such that every permutation of the digits of k is congruent to 3 (mod 4).

Original entry on oeis.org

11, 15, 19, 51, 55, 59, 91, 95, 99, 111, 115, 119, 151, 155, 159, 191, 195, 199, 511, 515, 519, 551, 555, 559, 591, 595, 599, 911, 915, 919, 951, 955, 959, 991, 995, 999, 1111, 1115, 1119, 1151, 1155, 1159, 1191, 1195, 1199, 1511, 1515, 1519, 1551, 1555, 1559
Offset: 11

Views

Author

Ctibor O. Zizka, Apr 30 2021

Keywords

Comments

Also numbers that contain only the digits 1,5,9. More general : Numbers k > 10 such that every permutation of the digits of k is congruent to r (mod m). For m = 4; r = 0 gives A343810, r = 1 gives A143967, r = 2 gives A284632, r = 3 gives this sequence.

Examples

			159 = 4*39 + 3, 195 = 4*48 + 3, 519 = 4*104 + 3, 591 = 4*147 + 3, 915 = 4*228 + 3, 951 = 4*237 + 3.

Crossrefs

Cf. A143967, A284632, A343810.

Programs

  • Mathematica
    Select[Range[11, 1600], AllTrue[Permutations[IntegerDigits[#]], Mod[FromDigits[#1], 4] == 3 &] &] (* Amiram Eldar, Apr 30 2021 *)
Showing 1-9 of 9 results.

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