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 1-8 of 8 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).

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).

A213084 Numbers consisting of ones and eights.

Original entry on oeis.org

1, 8, 11, 18, 81, 88, 111, 118, 181, 188, 811, 818, 881, 888, 1111, 1118, 1181, 1188, 1811, 1818, 1881, 1888, 8111, 8118, 8181, 8188, 8811, 8818, 8881, 8888, 11111, 11118, 11181, 11188, 11811, 11818, 11881, 11888, 18111, 18118, 18181, 18188, 18811, 18818
Offset: 1

Views

Author

Jens Ahlström, Jun 05 2012

Keywords

Comments

One and eight begin with vowels. The subsequence of primes begins 11, 181, 811, 1181, 1811, 8111. - Jonathan Vos Post, Jun 14 2012

Links

Crossrefs

Cf. A020456 (primes in this sequence).
Cf. numbers consisting of 1s and ks: A007088 (k=0), A007931 (k=2), A032917 (k=3), A032822 (k=4), A276037 (k=5), A284293 (k=6), A276039 (k=7), A284294 (k=9).

Programs

  • Mathematica
    Flatten[Table[FromDigits/@Tuples[{1,8},n],{n,5}]] (* Harvey P. Dale, Aug 27 2014 *)
  • PARI
    is(n) = #setintersect(vecsort(digits(n), , 8), [0, 2, 3, 4, 5, 6, 7, 9])==0 \\ Felix Fröhlich, Sep 09 2019
  • Python
    res = []
i = 0
while len (res) < 260:
    for c in str(i):
        if c in '18':
            continue
        else:
            break
    else:
        res.append(i)
    i = i + 1
print(res)
  • Python
    def a(n): return int(bin(n+1)[3:].replace('1', '8').replace('0', '1'))
print([a(n) for n in range(1, 45)]) # Michael S. Branicky, Jun 26 2025

A284294 Numbers using only digits 1 and 9.

Original entry on oeis.org

1, 9, 11, 19, 91, 99, 111, 119, 191, 199, 911, 919, 991, 999, 1111, 1119, 1191, 1199, 1911, 1919, 1991, 1999, 9111, 9119, 9191, 9199, 9911, 9919, 9991, 9999, 11111, 11119, 11191, 11199, 11911, 11919, 11991, 11999, 19111, 19119, 19191, 19199, 19911, 19919
Offset: 1

Views

Author

Jaroslav Krizek, Mar 25 2017

Keywords

Comments

Product of digits of terms is a power of 9; subsequence of A284295.
Prime terms are in A020457.

Links

Crossrefs

Cf. Numbers using only digits 1 and k for k = 0 and k = 2 - 9: A007088 (k = 0), A007931 (k = 2), A032917 (k = 3), A032822 (k = 4) , A276037 (k = 5), A284293 (k = 6), A276039 (k = 7), A213084 (k = 8), this sequence (k = 9).

Programs

  • Magma
    [n: n in [1..20000] | Set(IntegerToSequence(n, 10)) subset {1, 9}];
  • Mathematica
    Join @@ (FromDigits /@ Tuples[{1,9}, #] & /@ Range[5]) (* Giovanni Resta, Mar 25 2017 *)

Formula

The sum of first 2^n terms is (5*20^n + 38*10^n - 95*2^n + 1420)/171. - Giovanni Resta, Mar 25 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).

A385324 Numbers whose digits are all powers of the same single-digit base.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 28, 31, 33, 39, 41, 42, 44, 48, 51, 55, 61, 66, 71, 77, 81, 82, 84, 88, 91, 93, 99, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 124, 128, 131, 133, 139, 141, 142, 144, 148
Offset: 1

Views

Author

Stefano Spezia, Jun 25 2025

Keywords

Examples

			84 is a term since its digits 8 and 4 are both powers of 2.

Links

Crossrefs

Cf. A028846, A174813, A276037, A276039, A284293.
Cf. A385351 (subsequence)

Programs

  • Mathematica
    Select[Range[0,148],SubsetQ[{0},dig=IntegerDigits[#]]||SubsetQ[{1,2,4,8},dig]||SubsetQ[{1,3,9},dig]||SubsetQ[{1,5},dig]||SubsetQ[{1,6},dig]||SubsetQ[{1,7},dig] &]

Formula

{0} U A028846 U A174813 U A276037 U A276039 U A284293.
Showing 1-8 of 8 results.

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

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