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.

Previous Showing 11-16 of 16 results.

A284380 Numbers k with digits 5 and 7 only.

Original entry on oeis.org

5, 7, 55, 57, 75, 77, 555, 557, 575, 577, 755, 757, 775, 777, 5555, 5557, 5575, 5577, 5755, 5757, 5775, 5777, 7555, 7557, 7575, 7577, 7755, 7757, 7775, 7777, 55555, 55557, 55575, 55577, 55755, 55757, 55775, 55777, 57555, 57557, 57575, 57577, 57755, 57757
Offset: 1

Views

Author

Jaroslav Krizek, Mar 28 2017

Keywords

Links

Crossrefs

Prime terms are in A020467.
Numbers n with digits 5 and k only for k = 0 - 4 and 6 - 9: A169964 (k = 0), A276037 (k = 1), A072961 (k = 2), A284379 (k = 3), A256290 (k = 4), A256291 (k = 6), this sequence (k = 7), A284381 (k = 8), A284382 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {5, 7}];
  • Mathematica
    Join @@ ((FromDigits /@ Tuples[{5, 7}, #]) & /@ Range@ 5) (* Giovanni Resta, Mar 28 2017 *)
  • Python
    from sympy.utilities.iterables import multiset_permutations
def aupton(terms):
  n, digits, alst = 0, 1, []
  while len(alst) < terms:
    mpstr = "".join(d*digits for d in "57")
    for mp in multiset_permutations(mpstr, digits):
      alst.append(int("".join(mp)))
      if len(alst) == terms: break
    else: digits += 1
  return alst
print(aupton(44)) # Michael S. Branicky, May 07 2021

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

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).

A284381 Numbers k with digits 5 and 8 only.

Original entry on oeis.org

5, 8, 55, 58, 85, 88, 555, 558, 585, 588, 855, 858, 885, 888, 5555, 5558, 5585, 5588, 5855, 5858, 5885, 5888, 8555, 8558, 8585, 8588, 8855, 8858, 8885, 8888, 55555, 55558, 55585, 55588, 55855, 55858, 55885, 55888, 58555, 58558, 58585, 58588, 58855, 58858
Offset: 1

Views

Author

Jaroslav Krizek, Mar 28 2017

Keywords

Comments

All terms except the first are composite.

Links

Crossrefs

Numbers n with digits 5 and k only for k = 0 - 4 and 6 - 9: A169964 (k = 0), A276037 (k = 1), A072961 (k = 2), A284379 (k = 3), A256290 (k = 4), A256291 (k = 6), A284380 (k = 7), this sequence (k = 8), A284382 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {5, 8}];
  • Mathematica
    Join @@ ((FromDigits /@ Tuples[{5, 8}, #]) & /@ Range@ 5) (* Giovanni Resta, Mar 28 2017 *)
  • Python
    def a(n): return int(bin(n+1)[3:].replace('0', '5').replace('1', '8'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, May 08 2021

Formula

a(n) = (A284380(n)+A284382(n))/2. - Robert Israel, Mar 28 2017

A284382 Numbers k with digits 5 and 9 only.

Original entry on oeis.org

5, 9, 55, 59, 95, 99, 555, 559, 595, 599, 955, 959, 995, 999, 5555, 5559, 5595, 5599, 5955, 5959, 5995, 5999, 9555, 9559, 9595, 9599, 9955, 9959, 9995, 9999, 55555, 55559, 55595, 55599, 55955, 55959, 55995, 55999, 59555, 59559, 59595, 59599, 59955, 59959
Offset: 1

Views

Author

Jaroslav Krizek, Mar 28 2017

Keywords

Comments

Prime terms are in A020468.

Links

Crossrefs

Numbers n with digits 5 and k only for k = 0 - 4 and 6 - 9: A169964 (k = 0), A276037 (k = 1), A072961 (k = 2), A284379 (k = 3), A256290 (k = 4), A256291 (k = 6), A284380 (k = 7), A284381 (k = 8), this sequence (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {5, 9}];
  • Mathematica
    Join @@ ((FromDigits /@ Tuples[{5, 9}, #]) & /@ Range@ 5) (* Giovanni Resta, Mar 28 2017 *)
  • Python
    def a(n): return int(bin(n+1)[3:].replace('0', '5').replace('1', '9'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, May 09 2021

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).
Previous Showing 11-16 of 16 results.

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