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.

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A194389 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(11) and < > denotes fractional part.

Original entry on oeis.org

1, 17, 19, 20, 21, 23, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 55, 57, 58, 59, 61, 77, 79, 80, 81, 83, 93, 95, 96, 97, 98, 99, 100, 101, 102, 103, 105, 115, 117, 118, 119, 121, 137, 139, 140, 141, 143, 153, 155, 156, 157, 158, 159, 160, 161, 162, 163
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A010468, A194368, A194387, A194388.

Programs

  • Mathematica
    r = Sqrt[11]; c = 1/2;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t1, 1]]     (* A194387 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]     (* A194388 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]     (* A194389 *)

A194392 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) < 0, where r=sqrt(13) and < > denotes fractional part.

Original entry on oeis.org

1, 3, 29, 31, 33, 34, 35, 36, 37, 39, 41, 67, 69, 71, 72, 73, 74, 75, 77, 79, 105, 107, 143, 145, 181, 183, 209, 211, 213, 214, 215, 216, 217, 219, 221, 247, 249, 251, 252, 253, 254, 255, 257, 259, 285, 287, 323, 325, 361, 363, 389, 391, 393, 394, 395
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A010470, A194368, A194393, A194394.

Programs

  • Mathematica
    r = Sqrt[13]; c = 1/2;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t1, 1]]       (* A194392 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]       (* A194393 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]]       (* A194394 *)

A194393 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(13) and < > denotes fractional part.

Original entry on oeis.org

2, 4, 6, 8, 24, 26, 28, 30, 32, 38, 40, 42, 44, 46, 62, 64, 66, 68, 70, 76, 78, 80, 82, 84, 100, 102, 104, 106, 108, 110, 112, 138, 140, 142, 144, 146, 148, 150, 176, 178, 180, 182, 184, 186, 188, 204, 206, 208, 210, 212, 218, 220, 222, 224, 226, 242, 244
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A010470, A194368, A194392, A194394.

Programs

  • Mathematica
    r = Sqrt[13]; c = 1/2;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t1, 1]]       (* A194392 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]       (* A194393 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]]       (* A194394 *)

A194394 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(13) and < > denotes fractional part.

Original entry on oeis.org

5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 27, 43, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 65, 81, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 103, 109, 111, 113, 114, 115, 116, 117
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A010470, A194368, A194392, A194393.

Programs

  • Mathematica
    r = Sqrt[13]; c = 1/2;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t1, 1]]       (* A194392 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]       (* A194393 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]]       (* A194394 *)

A194395 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) < 0, where r=sqrt(14) and < > denotes fractional part.

Original entry on oeis.org

1, 5, 9, 13, 17, 21, 25, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 63, 67, 71, 75, 79, 83, 87, 121, 125, 129, 133, 137, 141, 145, 149, 151, 152, 153, 155, 156, 157, 159, 160, 161, 163, 164, 165, 167, 168, 169
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A010471, A194368, A194396, A194397.

Programs

  • Mathematica
    r = Sqrt[14]; c = 1/2;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t1, 1]]       (* A194395 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]       (* A194396 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t3, 1]]       (* A194397 *)

A194396 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(14) and < > denotes fractional part.

Original entry on oeis.org

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 34, 38, 42, 46, 50, 54, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 94, 98, 102, 106, 110, 114, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

Every term is even; see A194368.

Crossrefs

Cf. A010471, A194368, A194395, A194397.

Programs

  • Mathematica
    r = Sqrt[14]; c = 1/2;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t1, 1]]       (* A194395 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]       (* A194396 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t3, 1]]       (* A194397 *)

A194397 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(14) and < > denotes fractional part.

Original entry on oeis.org

3, 7, 11, 15, 19, 23, 27, 61, 65, 69, 73, 77, 81, 85, 89, 91, 92, 93, 95, 96, 97, 99, 100, 101, 103, 104, 105, 107, 108, 109, 111, 112, 113, 115, 116, 117, 119, 123, 127, 131, 135, 139, 143, 147, 181, 185, 189, 193, 197, 201, 205, 209, 211, 212, 213, 215
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Links

Crossrefs

Cf. A010471 (sqrt(14)), A194368, A194396, A194397.

Programs

  • Maple
    r:= sqrt(14):
X:= 0: R:= NULL: count:= 0:
for n from 1 while count < 100 do
  X:= X + frac(1/2+n*r) - frac(n*r);
  if X > 0 then
    count:= count+1;
    R:= R, n
  fi
od:
R; # Robert Israel, Nov 25 2020
  • Mathematica
    r = Sqrt[14]; c = 1/2;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t1, 1]]       (* A194395 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]       (* A194396 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t3, 1]]       (* A194397 *)

A194398 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) < 0, where r=sqrt(15) and < > denotes fractional part.

Original entry on oeis.org

1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 17, 18, 19, 20, 21, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 41, 42, 43, 44, 45, 49, 50, 51, 52, 53, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93
Offset: 1

Views

Author

Clark Kimberling, Aug 24 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A010472, A194368, A194399, A194400.

Programs

  • Mathematica
    r = Sqrt[15]; c = 1/2;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t1, 1]]       (* A194398 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t2, 1]]       (* A194399 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t3, 1]]       (* A194400 *)

A194399 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(15) and < > denotes fractional part.

Original entry on oeis.org

6, 8, 14, 16, 22, 24, 30, 32, 38, 40, 46, 48, 54, 56, 62, 70, 78, 86, 94, 102, 110, 118, 314, 322, 330, 338, 346, 354, 362, 370, 376, 378, 384, 386, 392, 394, 400, 402, 408, 410, 416, 418, 424, 426, 432, 434, 438, 442, 446, 450, 454, 458, 462, 466, 470
Offset: 1

Views

Author

Clark Kimberling, Aug 24 2011

Keywords

Comments

Every term is even; see A194368.

Crossrefs

Cf. A010472, A194368, A194398, A194400.

Programs

  • Mathematica
    r = Sqrt[15]; c = 1/2;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t1, 1]]       (* A194398 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t2, 1]]       (* A194399 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t3, 1]]       (* A194400 *)

A194400 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(15) and < > denotes fractional part.

Original entry on oeis.org

7, 15, 23, 31, 39, 47, 55, 377, 385, 393, 401, 409, 417, 425, 433, 439, 440, 441, 447, 448, 449, 455, 456, 457, 463, 464, 465, 471, 472, 473, 479, 480, 481, 487, 488, 489, 495, 503, 511, 519, 527, 535, 543, 551
Offset: 1

Views

Author

Clark Kimberling, Aug 24 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A010472, A194368, A194398, A194399.

Programs

  • Mathematica
    r = Sqrt[15]; c = 1/2;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t1, 1]]       (* A194398 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t2, 1]]       (* A194399 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t3, 1]]       (* A194400 *)
Previous Showing 31-40 of 67 results. Next

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