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 21-25 of 25 results.

A188057 Stanley Sequence S(0,9).

Original entry on oeis.org

0, 9, 10, 12, 13, 19, 21, 22, 27, 36, 37, 39, 40, 46, 48, 49, 81, 90, 91, 93, 94, 100, 102, 103, 108, 117, 118, 120, 121, 127, 129, 130, 243, 252, 253, 255, 256, 262, 264, 265, 270, 279, 280, 282, 283, 289, 291, 292, 324, 333, 334, 336, 337, 343, 345, 346, 351, 360, 361, 363, 364, 370, 372, 373, 729, 738, 739, 741, 742, 748
Offset: 1

Views

Author

N. J. A. Sloane, Mar 19 2011

Keywords

Comments

See A185256.

Links

Crossrefs

Cf. A185256.

A266728 Stanley sequence S_5(0,3).

Original entry on oeis.org

0, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 21, 25, 28, 29, 30, 31, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 46, 50, 53, 54, 55, 56, 58, 59, 60, 61, 63, 64, 65, 66, 68, 69, 71, 75, 78, 79, 80, 81, 83, 84, 85, 86, 88, 89, 90, 91, 93, 94, 96, 125, 128, 129, 130
Offset: 0

Views

Author

N. J. A. Sloane, Jan 04 2016

Keywords

Comments

Lexicographic first increasing sequence with a(0) = 0, a(1) = 3 and for all n > 1, {a(0), ..., a(n)} does not contain 5 terms in arithmetic progression.

Links

Crossrefs

Cf. A005836, A188053, A266727.
Cf. A185256 = S_3(0,3) = S(0,3), A267650 = S_4(0,3).

Programs

  • PARI
    A266728(n,show=1,L=5,v=[0,3],D=v->v[2..-1]-v[1..-2])={ while(#v<=n, show&&print1(v[#v]","); v=concat(v,v[#v]); while(v[#v]++, forvec(i=vector(L,j,[if(j1||next(2),2);break));v[n+1]} \\ M. F. Hasler, Jan 18 2016

Extensions

More terms from M. F. Hasler, Jan 18 2016

A236336 Lexicographically earliest increasing sequence of positive integers whose graph has no three collinear points.

Original entry on oeis.org

1, 2, 4, 5, 9, 12, 16, 22, 26, 33, 38, 45, 53, 60, 61, 76, 86, 91, 92, 97, 111, 112, 121, 134, 135, 147, 148, 150, 153, 157, 167, 180, 200, 212, 223, 227, 228, 238, 246, 264, 269, 282, 286, 305, 312, 313, 321, 322, 327, 328, 360, 374, 389, 393, 395, 420, 421
Offset: 1

Views

Author

Tanya Khovanova, Jan 22 2014

Keywords

Comments

An increasing version of A236335.

Examples

			Consider a(5). The previous terms are 1,2,4,5. The value of a(5) can't be 6 because points (3,4),(4,5),(5,6) (corresponding to values a(3),a(4),a(5)) are on the same line: y=x+1. Points (1,1),(3,4),(5,7) are on the same line y=3x/2-1/2, so a(5) can't be 7. Points (2,2),(3,4),(5,8) are on the same line: y=2x-2, so a(5) can't be 8. Thus a(5)=5.

Links

Crossrefs

Cf. A229037, A185256, A236335.

Programs

  • Maple
    a:= proc(n) option remember; local i, j, k, ok;
      if n<3 then n
    else for k from 1+a(n-1) do ok:=true;
           for j from n-1 to 2 by -1 while ok do
             for i from j-1 to 1 by -1 while ok do
               ok:= (n-j)*(a(j)-a(i))<>(j-i)*(k-a(j)) od
           od; if ok then return k fi
         od
      fi
    end:
seq(a(n), n=1..70);  # Alois P. Heinz, Jan 23 2014
  • Mathematica
    g[1] = 1;
g[n_] := g[n] =
  Min[Complement[Range[g[n - 1] + 1, 500],
    Select[Flatten[
      Table[g[k] + (n - k) (g[j] - g[k])/(j - k), {k, n - 2}, {j,
        k + 1, n - 1}]], IntegerQ[#] &]]]
Table[g[k], {k, 50}]

A236697 First differences of A131741.

Original entry on oeis.org

1, 2, 6, 2, 16, 2, 6, 4, 26, 6, 10, 6, 12, 6, 20, 12, 18, 22, 14, 34, 6, 30, 8, 10, 26, 24, 6, 42, 10, 8, 4, 8, 22, 2, 34, 24, 8, 10, 54, 8, 42, 28, 6, 96, 26, 40, 14, 60, 4, 20, 30, 46, 26, 12, 42, 28, 2, 70, 8, 126, 4, 26, 34, 6, 42, 18, 96, 26, 48, 4
Offset: 1

Views

Author

Zak Seidov, Jan 30 2014

Keywords

Comments

Among first 10000 terms, the largest is a(7790) = 17412.

Links

Crossrefs

Cf. A003002, A003003, A003278, A004793, A005047, A005487, A033157, A065825, A092482, A093678, A093679, A093680, A093681, A093682, A094870, A101884, A101886, A101888, A131741, A140577, A185256, A208746, A229037.

Formula

a(n) = A131741(n+1) - A131741(n).

A267650 Stanley sequence S_4(0,3): lexicographic first increasing sequence with a(0) = 0, a(1) = 3 and no 4 terms in arithmetic progression.

Original entry on oeis.org

0, 3, 4, 5, 7, 8, 10, 11, 16, 17, 18, 20, 21, 27, 28, 29, 31, 32, 34, 35, 36, 53, 55, 56, 57, 60, 61, 62, 64, 67, 69, 75, 87, 91, 100, 101, 103, 104, 105, 108, 109, 110, 114, 116, 120, 125, 127, 128, 129, 132, 134, 135, 164, 168, 173, 174, 175, 177, 181, 182, 184, 188, 190
Offset: 0

Views

Author

M. F. Hasler, Jan 18 2016

Keywords

Comments

See A185256 for S(0,3) = S_3(0,3) and A266728 for S_5(0,3).

Links

Crossrefs

For other examples of Stanley Sequences see A005487, A005836, A187843, A188052, A188053, A188054, A188055, A188056, A188057, A266727, A266728.
See also A004793, A033160, A033163.

Programs

  • PARI
    a(n,show=1,L=4,v=[0,3], D=v->v[2..-1]-v[1..-2])={while(#v<=n, show&&print1(v[#v]", "); v=concat(v, v[#v]); while(v[#v]++, forvec(i=vector(L, j, [if(j1||next(2), 2); break)); if(type(show)=="t_VEC", v, v[n+1])} \\ 2nd (optional) arg: zero = silent, nonzero = verbose, vector (e.g. [] or [1]) = get the whole list [a(1..n)] as return value, else just a(n). - M. F. Hasler, Jan 18 2016
Previous Showing 21-25 of 25 results.

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

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