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 1-10 of 10 results.

A028374 Numbers that have only curved digits {0, 3, 6, 8, 9} or digits that are both curved and linear {2, 5}.

Original entry on oeis.org

0, 2, 3, 5, 6, 8, 9, 20, 22, 23, 25, 26, 28, 29, 30, 32, 33, 35, 36, 38, 39, 50, 52, 53, 55, 56, 58, 59, 60, 62, 63, 65, 66, 68, 69, 80, 82, 83, 85, 86, 88, 89, 90, 92, 93, 95, 96, 98, 99, 200, 202, 203, 205, 206, 208, 209, 220, 222, 223, 225, 226, 228, 229, 230, 232, 233
Offset: 1

Views

Author

Greg Heil (gheil(AT)scn.org), Dec 11 1999

Keywords

Comments

From Bernard Schott, Mar 26 2023: (Start)
Previous name was: "Curved numbers: numbers that have only curved digits (0, 2, 3, 5, 6, 8, 9)"; but in fact, the curved numbers form the sequence A072960.
This sequence allows all digits except for 1, 4 and 7. (End)

Examples

			From _K. D. Bajpai_, Sep 07 2014: (Start)
206 is in the sequence because it has only curved digits 2, 0 and 6.
208 is in the sequence because it has only curved digits 2, 0 and 8.
2035689 is the smallest number having all the curved digits.
(End)

Links

Crossrefs

Cf. A028373 (straight digits: 1, 4, 7), A072960 (curved digits: 0, 3, 6, 8, 9), A072961 (both straight and curved digits: 2, 5).
Combinations: A082741 (digits: 1, 2, 4, 5, 7), A361780 (digits: 0, 1, 3, 4, 6, 7, 8, 9).
Cf. A034470 (subsequence of primes).

Programs

  • Magma
    [n: n in [0..300] | Set(Intseq(n)) subset [0,2,3,5, 6,8,9] ]; // Vincenzo Librandi, Sep 19 2014
  • Maple
    N:= 3: S:= {0, 2, 3, 5, 6, 8, 9}: K:= S:
for j from 2 to N do
     K:= map(t -> seq(10*t+s, s=S), K);
         od:
print( K);  # K. D. Bajpai, Sep 07 2014
  • Mathematica
    f[n_] := Block[{id = IntegerDigits[n], curve = {0, 2, 3, 5, 6, 8, 9}}, If[ Union[ Join[id, curve]] == curve, True, False]]; Select[ Range[0, 240], f[ # ] & ]
Select[Range[0, 249], Union[DigitCount[#] * {1, 0, 0, 1, 0, 0, 1, 0, 0, 0}] == {0} &] (* Alonso del Arte, May 23 2014 *)
Select[Range[0,500],Intersection[IntegerDigits[#],{1,4,7}]=={}&] (* K. D. Bajpai, Sep 07 2014 *)
  • Python
    for n in range(10**3):
  s = str(n)
  if not (s.count('1') + s.count('4') + s.count('7')):
    print(n,end=', ') # Derek Orr, Sep 19 2014

Extensions

Corrected and extended by Rick L. Shepherd, May 21 2003
Offset corrected by Arkadiusz Wesolowski, Aug 15 2011
Definition clarified by Bernard Schott, Mar 25 2023

A284379 Numbers k with digits 3 and 5 only.

Original entry on oeis.org

3, 5, 33, 35, 53, 55, 333, 335, 353, 355, 533, 535, 553, 555, 3333, 3335, 3353, 3355, 3533, 3535, 3553, 3555, 5333, 5335, 5353, 5355, 5533, 5535, 5553, 5555, 33333, 33335, 33353, 33355, 33533, 33535, 33553, 33555, 35333, 35335, 35353, 35355, 35533, 35535
Offset: 1

Views

Author

Jaroslav Krizek, Mar 26 2017

Keywords

Comments

Prime terms are in A020462.

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), this sequence (k = 3), A256290 (k = 4), A256291 (k = 6), A284380 (k = 7), A284381 (k = 8), A284382 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {3, 5}];
  • Maple
    A:= 3,5: B:= [3,5];
for i from 1 to 5 do
  B:= map(t -> (10*t+3,10*t+5), B);
  A:= A, op(B);
od:
A; # Robert Israel, Apr 13 2020
  • Mathematica
    Select[Range[35600], Times @@ Boole@ Map[MemberQ[{3, 5}, #] &, IntegerDigits@ #] > 0 &] (* or *)
Table[FromDigits /@ Union@ Apply[Join, Map[Permutations@ # &, Tuples[{3, 5}, n]]], {n, 5}] // Flatten (* Michael De Vlieger, Mar 27 2017 *)

Formula

From Robert Israel, Apr 13 2020: (Start)
a(n) = 2*A007931(n)+A002275(n).
a(2n+1) = 10*a(n)+3.
a(2n+2) = 10*a(n)+5.
G.f. g(x) satisfies g(x) = 10*(x^2+x)*g(x^2) + (3*x+5*x^2)/(1-x^2). (End)

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

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).

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 *)

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

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 *)

A361780 Numbers that have digits consisting only of line segments {1, 4, 7} or curved digits {0, 3, 6, 8, 9}.

Original entry on oeis.org

0, 1, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 19, 30, 31, 33, 34, 36, 37, 38, 39, 40, 41, 43, 44, 46, 47, 48, 49, 60, 61, 63, 64, 66, 67, 68, 69, 70, 71, 73, 74, 76, 77, 78, 79, 80, 81, 83, 84, 86, 87, 88, 89, 90, 91, 93, 94, 96, 97, 98, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110
Offset: 1

Views

Author

Bernard Schott, Mar 23 2023

Keywords

Comments

This sequence allows all digits except for 2 and 5.

Crossrefs

Cf. A028373 (line-segment digits: {1, 4, 7}), A072960 (curved digits: {0, 3, 6, 8, 9}), A072961 (both line segments and curves digits: {2, 5}).
Cf. A082741 (digits: {1, 2, 4, 5, 7}), A028374 (digits: {0, 2, 3, 5, 6, 8, 9}), this sequence (digits {0, 1, 3, 4, 6, 7, 8, 9}).

Programs

  • Mathematica
    Select[Range[0, 110], AllTrue[IntegerDigits[#], ! MemberQ[{2, 5}, #1] &] &] (* Amiram Eldar, Mar 24 2023 *)
Showing 1-10 of 10 results.

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