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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A194425 Numbers m such that Sum_{k=1..m} (<2/3 + k*r> - ) > 0, where r=sqrt(2) and < > denotes fractional part.

Original entry on oeis.org

5, 8, 10, 11, 17, 20, 22, 23, 29, 32, 34, 35, 37, 38, 39, 40, 41, 44, 46, 47, 49, 50, 51, 52, 53, 56, 58, 59, 61, 62, 63, 64, 65, 68, 80, 92, 104, 107, 109, 110, 116, 119, 121, 122, 128, 131, 133, 134, 136, 137, 138, 139, 140, 143, 145, 146, 148, 149, 150
Offset: 1

Views

Author

Clark Kimberling, Aug 24 2011

Keywords

Comments

See A194368.

Links

Crossrefs

Cf. A194368.

Programs

  • Mathematica
    r = Sqrt[2]; c = 2/3;
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, 300}];
Flatten[Position[t1, 1]]         (* A194422 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]         (* A194423 *)
%/3         (* A194424 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t3, 1]]         (* A194425 *)

A194371 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) < 0, where r=sqrt(3) and fractional part is denoted by < >.

Original entry on oeis.org

1, 5, 9, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 31, 35, 39, 57, 61, 65, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 87, 91, 95, 113, 117, 121, 125, 127, 128, 129, 131, 132, 133, 135, 136, 137, 139, 143, 147, 151, 169, 173, 177, 181, 183, 184, 185, 187
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Links

Crossrefs

Cf. A194368.

Programs

  • Mathematica
    r = Sqrt[3]; 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]]  (* A194371 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t2, 1]] (* A194372 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]] (* A194373 *)

A194372 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(3) and < > denotes fractional part.

Original entry on oeis.org

2, 4, 6, 8, 10, 12, 14, 18, 22, 26, 28, 30, 32, 34, 36, 38, 40, 42, 46, 50, 54, 56, 58, 60, 62, 64, 66, 68, 70, 74, 78, 82, 84, 86, 88, 90, 92, 94, 96, 98, 102, 106, 110, 112, 114, 116, 118, 120, 122, 124, 126, 130, 134, 138, 140, 142, 144, 146, 148, 150, 152
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Links

Crossrefs

Cf. A194368, A194371.

Programs

  • Mathematica
    r = Sqrt[3]; 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]]  (* A194371 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t2, 1]] (* A194372 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]] (* A194373 *)

A194373 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(3) and < > denotes fractional part.

Original entry on oeis.org

3, 7, 11, 29, 33, 37, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 59, 63, 67, 85, 89, 93, 97, 99, 100, 101, 103, 104, 105, 107, 108, 109, 111, 115, 119, 123, 141, 145, 149, 153, 155, 156, 157, 159, 160, 161, 163, 164, 165, 167, 171, 175, 179, 197
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Links

Crossrefs

Cf. A194368, A194371.

Programs

  • Mathematica
    r = Sqrt[3]; 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]]  (* A194371 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t2, 1]] (* A194372 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]] (* A194373 *)
  • PARI
    isok(n) = sum(k=1, n, frac(1/2+k*sqrt(3)) - frac(k*sqrt(3))) > 0; \\ Michel Marcus, Sep 10 2018

A194378 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) < 0, where r=sqrt(7) and < > denotes fractional part.

Original entry on oeis.org

1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 35, 37, 38, 39, 40, 41, 43, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 83, 85, 86, 87, 88, 89, 91, 97, 99, 100
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A194368, A194379, A194380.

Programs

  • Mathematica
    r = Sqrt[7]; 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]]   (* A194378 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]  (* A194379 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t3, 1]]   (* A194380 *)

A194379 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(7) and < > denotes fractional part.

Original entry on oeis.org

2, 14, 16, 28, 30, 32, 34, 36, 42, 44, 46, 48, 50, 62, 64, 76, 78, 80, 82, 84, 90, 92, 94, 96, 98, 110, 112, 124, 126, 128, 130, 132, 138, 140, 142, 144, 146, 158, 160, 172, 174, 176, 178, 180, 186, 188, 190, 192, 194, 206, 208, 220, 222, 224, 226, 228
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

All the terms are even. See A194368.

Examples

			r = Sqrt[7]; c = 1/2;

Crossrefs

Cf. A194368.

Programs

  • Mathematica
    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]]   (* A194378 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]  (* A194379 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t3, 1]]   (* A194380 *)

A194380 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(7) and < > denotes fractional part.

Original entry on oeis.org

31, 33, 45, 47, 79, 81, 93, 95, 127, 129, 141, 143, 175, 177, 189, 191, 223, 225, 237, 239, 525, 527, 539, 541, 573, 575, 587, 589, 621, 623, 635, 637, 669, 671, 683, 685, 717, 719, 731, 733
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A194368, A194378, A194379.

Programs

  • Mathematica
    r = Sqrt[7]; 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]]   (* A194378 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]  (* A194379 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t3, 1]]   (* A194380 *)

A194386 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(10) and < > denotes fractional part.

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, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A010467, A194368, A194385.

Programs

  • Mathematica
    r = Sqrt[10]; 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, 300}];
Flatten[Position[t1, 1]]   (* empty *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t2, 1]]     (* A194385 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]]     (* A194386 *)

A194387 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

3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 25, 27, 28, 29, 31, 47, 49, 50, 51, 53, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 85, 87, 88, 89, 91, 107, 109, 110, 111, 113, 123, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 145, 147, 148, 149, 151, 167, 169, 170
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A010468, A194368, A194388, A194389.

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 *)

A194388 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

2, 4, 14, 16, 18, 22, 24, 26, 30, 32, 34, 44, 46, 48, 52, 54, 56, 60, 62, 64, 74, 76, 78, 82, 84, 86, 90, 92, 94, 104, 106, 108, 112, 114, 116, 120, 122, 124, 134, 136, 138, 142, 144, 146, 150, 152, 154, 164, 166, 168, 172, 174, 176, 180, 182, 184, 194, 196
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

Every term is even; see A194368.

Crossrefs

Cf. A010468, A194368, A194387, A194389.

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 *)
Previous Showing 21-30 of 67 results. Next

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