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 11 results. Next

A031941 Numbers without consecutive equal base 3 digits.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 10, 11, 15, 16, 19, 20, 21, 23, 30, 32, 33, 34, 46, 47, 48, 50, 57, 59, 60, 61, 64, 65, 69, 70, 91, 92, 96, 97, 100, 101, 102, 104, 138, 140, 141, 142, 145, 146, 150, 151, 172, 173, 177, 178, 181, 182, 183, 185, 192
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

Essentially the same as A043089, b.t.w. the initial "0" could be as well included here. Also: numbers n such that A043277(n)=1. - M. F. Hasler, Jul 23 2013

Crossrefs

Cf. A000975 (base-2 analog), A031942 or A043090 (base-4 analog), A031943 or A043091 (base-5 analog), A043092, ..., A043096 (base-6 through base-10 analog).

Programs

  • Mathematica
    Select[Range[200],FreeQ[Differences[IntegerDigits[#,3]],0]&] (* Harvey P. Dale, Mar 03 2024 *)
  • PARI
    for(i=1,199,A043277(i)==1 & print1(i",")) \\ - M. F. Hasler, Jul 23 2013

Formula

A031941 = { n | A043277(n)=1 } = A043089 \ {0}. - M. F. Hasler, Jul 23 2013

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010

A043091 Every string of 2 consecutive base 5 digits contains exactly 2 distinct numbers.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 26, 27, 28, 29, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 57, 58, 59, 65, 66, 67, 69, 70, 71, 72, 73, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86
Offset: 0

Views

Author

Clark Kimberling

Keywords

Programs

  • Mathematica
    Select[Range[0,100],FreeQ[Differences[IntegerDigits[#,5]],0]&] (* Harvey P. Dale, Apr 04 2015 *)

Formula

A031943 UNION {0}. [From R. J. Mathar, Oct 20 2008]

A031942 Numbers with no consecutive equal base 4 digits.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 17, 18, 19, 24, 25, 27, 28, 29, 30, 33, 34, 35, 36, 38, 39, 44, 45, 46, 49, 50, 51, 52, 54, 55, 56, 57, 59, 68, 70, 71, 72, 73, 75, 76, 77, 78, 97, 98, 99, 100, 102, 103, 108, 109, 110, 113, 114, 115
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A000975 (base-2 analog), A031941 or A043089 (base-3 analog), A031943 or A043091 (base-5 analog), A043092, ..., A043096 (base-6 through base-10 analog).

Formula

A031942 = { n | A043278(n)=1 } = A043090 \ {0}. - M. F. Hasler, Jul 23 2013

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010

A108120 Floor[n*1/Sin[1]], or Beatty sequence for 1/sin(1).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 83, 84, 85
Offset: 1

Views

Author

Zak Seidov, Jun 04 2005

Keywords

Comments

Complement of A108587; not the same as A108586: a(37)=43 <> A108586(37)=44. - Reinhard Zumkeller, Jun 11 2005

Crossrefs

Cf. A023800, A031943, A037918, A039215, A043091, A047253.
Cf. A108593.

Programs

  • Mathematica
    a[n_]:=Floor[n*1/Sin[1]];Table[a[n], {n, 90}]

Formula

a(n) = floor(n*1/sin(1))

A043092 Numbers in which every string of 2 consecutive base 6 digits contains exactly 2 distinct numbers.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 48, 49, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 73, 74, 75, 76, 77, 78, 80
Offset: 1

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A000975 (base-2 analog), A031941 or A043089 (base-3 analog), A031942 or A043090 (base-4 analog), A031943 or A043091 (base-5 analog), A043093, ..., A043096 (base-7 through base-10 analog).

Programs

  • Mathematica
    Select[Range[0,80],FreeQ[Differences[IntegerDigits[#,6]],0]&] (* Harvey P. Dale, Sep 09 2016 *)

A043095 Numbers with property that no two consecutive base 9 digits are equal.

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, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 82
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A000975 (base-2 analog), A031941 or A043089 (base-3 analog), A031942 or A043090 (base-4 analog), A031943 or A043091 (base-5 analog), A043092, ..., A043096 (base-6 through base-10 analog).
Cf. A023804 (subsequence).

Programs

  • Maple
    isA043095 := proc(n)
    dgs := convert(n,base,9) ;
    for i from 2 to nops(dgs) do
        if op(i,dgs) = op(i-1,dgs) then
            return false;
        end if;
    end do:
    true ;
end proc:
A043095 := proc(n)
    option remember;
    if n =1 then
        0;
    else
        for a from procname(n-1)+1 do
            if isA043095(a) then
                return a;
            end if;
        end do;
    end if;
end proc:
seq(A043095(n),n=1..120) ; # R. J. Mathar, Dec 28 2023
  • Mathematica
    Select[Range[0,100],!MemberQ[Flatten[Differences/@Partition[ IntegerDigits[ #,9],2,1]],0]&] (* Harvey P. Dale, Apr 05 2014 *)
  • PARI
    isok(n) = {my(d = digits(n, 9)); for (i=2, #d, if (d[i] == d[i-1], return (0));); return (1);} \\ Michel Marcus, Oct 11 2017

A108611 Excess of Beatty-function of 1/sin(1) over n.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16
Offset: 0

Views

Author

Zak Seidov, Jun 13 2005

Keywords

Crossrefs

Cf. A023800, A031943, A037918, A039215, A043091, A047253, A108120.

Formula

a(n) = A108120[n] - n.

A043093 Every string of 2 consecutive base 7 digits contains exactly 2 distinct numbers.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 63, 64, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78
Offset: 0

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A000975 (base-2 analog), A031941 or A043089 (base-3 analog), A031942 or A043090 (base-4 analog), A031943 or A043091 (base-5 analog), A043092, ..., A043096 (base-6 through base-10 analog).

A108612 Beatty-2 (or nested Beatty) sequence for 1/sin(1).

Original entry on oeis.org

1, 4, 9, 16, 25, 42, 56, 72, 90, 110, 143, 168, 195, 224, 255, 304, 340, 378, 418, 460, 504, 572, 621, 672, 725, 780, 864, 924, 986, 1050, 1116, 1216, 1287, 1360, 1435, 1512, 1591, 1710, 1794, 1880, 1968, 2058, 2193, 2288, 2385, 2484, 2585, 2736, 2842, 2950
Offset: 1

Views

Author

Zak Seidov, Jun 13 2005

Keywords

Crossrefs

Cf. A023800, A031943, A037918, A039215, A043091, A047253, A108120, A108611, A108613.

Formula

a(n) = floor(n*floor(n/sin(1))).

A108613 Excess of Beatty-2 function of 1/sin(1) over n^2.

Original entry on oeis.org

0, 0, 0, 0, 0, 6, 7, 8, 9, 10, 22, 24, 26, 28, 30, 48, 51, 54, 57, 60, 63, 88, 92, 96, 100, 104, 135, 140, 145, 150, 155, 192, 198, 204, 210, 216, 222, 266, 273, 280, 287, 294, 344, 352, 360, 368, 376, 432, 441, 450, 459, 468, 477, 540, 550, 560, 570, 580, 649, 660
Offset: 0

Views

Author

Zak Seidov, Jun 13 2005

Keywords

Comments

Cf. A108612 Beatty-2 (or nested Beatty) function of 1/sin(1).

Crossrefs

Cf. A023800, A031943, A037918, A039215, A043091, A047253, A108120, A108611, A108612.

Formula

a(n) = A108612[n] - n^2 = floor(n*floor(n/sin(1))) - n^2.
Showing 1-10 of 11 results. Next

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