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 1-5 of 5 results.

A240116 Schoenheim lower bound L(n,5,2).

Original entry on oeis.org

1, 3, 3, 4, 4, 6, 7, 8, 8, 12, 12, 13, 14, 18, 19, 20, 21, 27, 28, 29, 30, 37, 38, 40, 41, 48, 50, 52, 53, 62, 63, 65, 67, 76, 78, 80, 82, 93, 95, 97, 99, 111, 113, 116, 118, 130, 133, 136, 138, 152, 154, 157, 160, 174, 177, 180, 183, 199, 202, 205, 208, 225
Offset: 5

Views

Author

Colin Barker, Apr 01 2014

Keywords

Links

Crossrefs

Cf. A240115, A240117, A240118, A240119.
Cf. A011975, A011977, A036831, A036832, A036833, A036834, A036835, A036836.

Programs

  • Mathematica
    schoenheim[n_, k_, t_] := Module[{lb = 1, n1 = n, k1 = k, t1 = t}, n1 += 1 - t1; k1 += 1 - t1; While[t1 > 0, lb = Ceiling[(lb*n1)/k1]; t1--; n1++; k1++]; lb];
Table[schoenheim[n, 5, 2], {n, 5, 100}] (* Jean-François Alcover, Jan 26 2019, from PARI *)
  • PARI
    schoenheim(n, k, t) = {
  my(lb = 1);
  n += 1-t; k += 1-t;
  while(t>0,
    lb = ceil((lb*n)/k);
    t--; n++; k++
  );
  lb
}
s=[]; for(n=5, 100, s=concat(s, schoenheim(n, 5, 2))); s

Formula

Empirical g.f.: x^5*(x^24 -x^21 -x^20 +2*x^17 +x^14 +x^12 -x^10 +2*x^9 +x^6 -x^4 +x^3 +2*x +1) / ( -x^25 +x^24 +x^21 -x^20 +x^5 -x^4 -x +1).
a(n) = ceiling((n/5)*ceiling((n-1)/4)). - Nathaniel Johnston, Jan 10 2024

A240117 Schoenheim lower bound L(n,6,2).

Original entry on oeis.org

1, 3, 3, 3, 4, 4, 6, 7, 7, 8, 8, 12, 12, 13, 14, 14, 19, 20, 20, 21, 22, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 50, 51, 52, 54, 55, 63, 65, 66, 68, 69, 79, 80, 82, 84, 85, 96, 98, 99, 101, 103, 114, 116, 118, 120, 122, 135, 137, 139, 141, 143, 157, 159, 161
Offset: 6

Views

Author

Colin Barker, Apr 01 2014

Keywords

Links

Crossrefs

Cf. A240115, A240116, A240118, A240119.
Cf. A011975, A036831, A036832, A036833, A036834, A036835, A036836.

Programs

  • Mathematica
    schoenheim[n_, k_, t_] := Module[{lb = 1, n1 = n, k1 = k, t1 = t}, n1 += 1 - t1; k1 += 1 - t1; While[t1 > 0, lb = Ceiling[(lb*n1)/k1]; t1--; n1++; k1++]; lb];
Table[schoenheim[n, 6, 2], {n, 6, 100}] (* Jean-François Alcover, Jan 26 2019, from PARI *)
  • PARI
    schoenheim(n, k, t) = {
  my(lb = 1);
  n += 1-t; k += 1-t;
  while(t>0,
    lb = ceil((lb*n)/k);
    t--; n++; k++
  );
  lb
}
s=[]; for(n=6, 100, s=concat(s, schoenheim(n, 6, 2))); s

Formula

Empirical g.f.: x^6*(x^35 -x^31 -x^30 +2*x^26 +x^23 +x^20 -x^18 +x^17 +x^16 +x^13 -x^12 +2*x^11 +x^7 -x^5 +x^4 +2*x +1) / ( -x^36 +x^35 +x^31 -x^30 +x^6 -x^5 -x +1).

A240118 Schoenheim lower bound L(n,5,3).

Original entry on oeis.org

1, 4, 5, 7, 11, 14, 18, 27, 32, 37, 54, 61, 68, 94, 103, 116, 147, 163, 180, 221, 240, 260, 319, 342, 366, 438, 465, 500, 581, 619, 658, 756, 800, 844, 968, 1016, 1066, 1210, 1265, 1329, 1485, 1555, 1627, 1805, 1882, 1960, 2173, 2257, 2343, 2582, 2673, 2778
Offset: 5

Views

Author

Colin Barker, Apr 01 2014

Keywords

Links

Crossrefs

Cf. A240115, A240116, A240117, A240119.
Cf. A011975, A036831, A036832, A036833, A036834, A036835, A036836.

Programs

  • Mathematica
    schoenheim[n_, k_, t_] := Module[{lb = 1, n1 = n, k1 = k, t1 = t}, n1 += 1 - t1; k1 += 1 - t1; While[t1 > 0, lb = Ceiling[(lb*n1)/k1]; t1--; n1++; k1++]; lb];
Table[schoenheim[n, 5, 3], {n, 5, 100}] (* Jean-François Alcover, Jan 26 2019, from PARI *)
  • PARI
    schoenheim(n, k, t) = {
  my(lb = 1);
  n += 1-t; k += 1-t;
  while(t>0,
    lb = ceil((lb*n)/k);
    t--; n++; k++
  );
  lb
}
s=[]; for(n=5, 100, s=concat(s, schoenheim(n, 5, 3))); s

A240119 Schoenheim lower bound L(n,6,3).

Original entry on oeis.org

1, 4, 4, 6, 7, 11, 14, 18, 19, 30, 32, 37, 42, 57, 64, 70, 77, 104, 112, 121, 130, 167, 178, 194, 205, 248, 267, 286, 301, 362, 378, 401, 425, 494, 520, 547, 574, 667, 697, 728, 759, 870, 904, 948, 984, 1105, 1153, 1202, 1242, 1394, 1438, 1492, 1547, 1711
Offset: 6

Views

Author

Colin Barker, Apr 01 2014

Keywords

Links

Crossrefs

Cf. A240115, A240116, A240117, A240118.
Cf. A011975, A036831, A036832, A036833, A036834, A036835, A036836.

Programs

  • Mathematica
    schoenheim[n_, k_, t_] := Module[{lb = 1, n1 = n, k1 = k, t1 = t}, n1 += 1 - t1; k1 += 1 - t1; While[t1 > 0, lb = Ceiling[(lb*n1)/k1]; t1--; n1++; k1++]; lb];
Table[schoenheim[n, 6, 3], {n, 6, 100}] (* Jean-François Alcover, Jan 26 2019, from PARI *)
  • PARI
    schoenheim(n, k, t) = {
  my(lb = 1);
  n += 1-t; k += 1-t;
  while(t>0,
    lb = ceil((lb*n)/k);
    t--; n++; k++
  );
  lb
}
s=[]; for(n=6, 100, s=concat(s, schoenheim(n, 6, 3))); s

A011976 Covering numbers C(n,4,2).

Original entry on oeis.org

1, 3, 3, 5, 6, 8, 9, 11, 12, 13, 18, 19, 20, 26, 27, 31, 35, 37, 39, 46, 48, 50, 59, 61, 63, 73, 75, 78, 88, 91, 94, 105, 108, 111, 124, 127, 130, 144, 147, 151, 165, 169, 173, 188, 192, 196, 213, 217, 221, 239, 243, 248, 266, 271, 276, 295, 300, 305, 326
Offset: 4

Views

Author

N. J. A. Sloane

Keywords

Comments

Only differs from A240115 when n = 7, 9, 10, or 19. - Nathaniel Johnston, Jan 10 2024

References

  • CRC Handbook of Combinatorial Designs, 1996, p. 262.

Links

Crossrefs

Cf. A011975, A011977.

Extensions

a(21)-a(62) from Nathaniel Johnston, Jan 10 2024
Showing 1-5 of 5 results.

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

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