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 1-7 of 7 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).

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).

A284971 Numbers with digits 4 and 7 only.

Original entry on oeis.org

4, 7, 44, 47, 74, 77, 444, 447, 474, 477, 744, 747, 774, 777, 4444, 4447, 4474, 4477, 4744, 4747, 4774, 4777, 7444, 7447, 7474, 7477, 7744, 7747, 7774, 7777, 44444, 44447, 44474, 44477, 44744, 44747, 44774, 44777, 47444, 47447, 47474, 47477, 47744, 47747
Offset: 1

Views

Author

Jaroslav Krizek, Apr 07 2017

Keywords

Crossrefs

Prime terms are in A020465.
Numbers with digits 4 and k only for k = 0 - 3 and 5 - 9: A169967 (k = 0), A032822 (k = 1), A284920 (k = 2), A032834 (k = 3), A256290 (k = 5), A284634 (k = 6), this sequence (k = 7), A284972 (k = 8), A284973 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {4, 7}]
  • Mathematica
    Flatten@ Table[FromDigits /@ Tuples[{4, 7}, n], {n, 5}] (* Giovanni Resta, Apr 08 2017 *)
  • PARI
    is(n) = my(x=Set([4, 7]), y=Set([0, 1, 2, 3, 5, 6, 8, 9])); if(#setintersect(Set(digits(n)), x) > 0 && #setintersect(Set(digits(n)), y)==0, return(1)); 0 \\ Felix Fröhlich, Apr 08 2017
  • Python
    def a(n):
  b = bin(n+1)[3:]
  return int("".join(b.replace("0", "4").replace("1", "7")))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, Apr 07 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).

A284973 Numbers with digits 4 and 9 only.

Original entry on oeis.org

4, 9, 44, 49, 94, 99, 444, 449, 494, 499, 944, 949, 994, 999, 4444, 4449, 4494, 4499, 4944, 4949, 4994, 4999, 9444, 9449, 9494, 9499, 9944, 9949, 9994, 9999, 44444, 44449, 44494, 44499, 44944, 44949, 44994, 44999, 49444, 49449, 49494, 49499, 49944, 49949
Offset: 1

Views

Author

Jaroslav Krizek, Apr 07 2017

Keywords

Crossrefs

Prime terms are in A020466.
Numbers with digits 4 and k only for k = 0 - 3 and 5 - 9: A169967 (k = 0), A032822 (k = 1), A284920 (k = 2), A032834 (k = 3), A256290 (k = 5), A284634 (k = 6), A284971 (k = 7), A284972 (k = 8), this sequence (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {4, 9}]
  • PARI
    a(n,{p=[4,9]})={my(v=binary(n+1));fromdigits(vector(#v-1,i,p[2]*v[i+1]+p[1]*!v[i+1]))} \\ R. J. Cano, Apr 09 2017

A284972 Numbers with digits 4 and 8 only.

Original entry on oeis.org

4, 8, 44, 48, 84, 88, 444, 448, 484, 488, 844, 848, 884, 888, 4444, 4448, 4484, 4488, 4844, 4848, 4884, 4888, 8444, 8448, 8484, 8488, 8844, 8848, 8884, 8888, 44444, 44448, 44484, 44488, 44844, 44848, 44884, 44888, 48444, 48448, 48484, 48488, 48844, 48848
Offset: 1

Views

Author

Jaroslav Krizek, Apr 07 2017

Keywords

Comments

All terms are even.

Crossrefs

Numbers with digits 4 and k only for k = 0 - 3 and 5 - 9: A169967 (k = 0), A032822 (k = 1), A284920 (k = 2), A032834 (k = 3), A256290 (k = 5), A284634 (k = 6), A284971 (k = 7), this sequence (k = 8), A284973 (k = 9).

Programs

  • Magma
    [n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {4, 8}]
  • Mathematica
    Flatten@ Table[FromDigits /@ Tuples[{4, 8}, n], {n, 5}] (* Giovanni Resta, Apr 07 2017 *)
  • PARI
    a(n) = my (b = binary(1+n)); b[1] = 0; return (4*(10^(#b-1)-1)/(10-1) + (8-4)*fromdigits(b)) \\ Rémy Sigrist, Apr 08 2017
  • PARI
    a(n)={my(v=binary(n+1));v[1]=0;v+=vector(#v,i,i>1);4*fromdigits(v)} \\ R. J. Cano, Apr 08 2017
  • PARI
    a(n,{p=[4,8]})={my(v=binary(n+1));fromdigits(vector(#v-1,i,p[2]*v[i+1]+p[1]*!v[i+1]))} \\ R. J. Cano, Apr 09 2017

Formula

a(n) = 2 * A284920(n) = 4 * A032822(n).
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.