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 67 results. Next

A194369 (A194368)/2.

Original entry on oeis.org

1, 2, 6, 7, 8, 12, 13, 14, 35, 36, 37, 41, 42, 43, 47, 48, 49, 70, 71, 72, 76, 77, 78, 82, 83, 84, 204, 205, 206, 210, 211, 212, 216, 217, 218, 239, 240, 241, 245, 246, 247, 251, 252, 253, 274, 275, 276, 280, 281, 282, 286
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A194368.

Programs

  • Mathematica
    r = Sqrt[2]; 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]]  (* empty *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t2, 1]] (* A194368 *)
%/2 (* A194369 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]] (* A194370 *)

A194402 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=(1+sqrt(5))/2 and < > denotes fractional part.

Original entry on oeis.org

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 26, 28, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 60, 62, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 98, 100, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 132, 134, 140, 142, 144, 146, 148, 150, 152, 154
Offset: 1

Views

Author

Clark Kimberling, Aug 24 2011

Keywords

Comments

Every term is even; see A194368 and A194403.

Crossrefs

Cf. A001622, A194368, A194401, A194403, A194404.

Programs

  • Mathematica
    r = GoldenRatio; 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]]       (* A194401 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]       (* A194402 *)
%/2       (* A194403 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]       (* A194404 *)

A194381 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) < 0, where r=sqrt(8) and < > denotes fractional part.

Original entry on oeis.org

1, 2, 3, 7, 8, 9, 13, 14, 15, 19, 20, 21, 25, 26, 27, 31, 32, 33, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A010466, A194368, A194382, A194383, A194384.

Programs

  • Mathematica
    r = Sqrt[8]; 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]]   (* A194381 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]   (* A194382 *)
%/2  (* A194383 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 600}];
Flatten[Position[t3, 1]]   (* A194384 *)

A194382 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(8) and < > denotes fractional part.

Original entry on oeis.org

4, 6, 10, 12, 16, 18, 22, 24, 28, 30, 34, 40, 46, 52, 58, 64, 104, 110, 116, 122, 128, 134, 138, 140, 144, 146, 150, 152, 156, 158, 162, 164, 168, 170, 172, 176, 178, 182, 184, 188, 190, 194, 196, 200, 202, 204, 208, 210, 214, 216, 220, 222, 226, 228
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A010466, A194368, A194383.

Programs

  • Mathematica
    r = Sqrt[8]; 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]]   (* A194381 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]   (* A194382 *)
%/2  (* A194383 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 600}];
Flatten[Position[t3, 1]]   (* A194384 *)

A194383 a(n) = (1/2) * A194382(n).

Original entry on oeis.org

2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 20, 23, 26, 29, 32, 52, 55, 58, 61, 64, 67, 69, 70, 72, 73, 75, 76, 78, 79, 81, 82, 84, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 100, 101, 102, 104, 105, 107, 108, 110, 111, 113, 114, 116, 117, 119, 122, 125, 128, 131, 134
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A194368, A194382.

Programs

  • Mathematica
    r = Sqrt[8]; 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]]   (* A194381 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]   (* A194382 *)
%/2  (* A194383 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 600}];
Flatten[Position[t3, 1]]   (* A194384 *)

A194384 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=sqrt(8) and < > denotes fractional part.

Original entry on oeis.org

5, 11, 17, 23, 29, 139, 145, 151, 157, 163, 169, 173, 174, 175, 179, 180, 181, 185, 186, 187, 191, 192, 193, 197, 198, 199, 203, 209, 215, 221, 227, 233, 343, 349, 355, 361, 367, 373, 377, 378, 379, 383, 384, 385, 389, 390, 391, 395, 396, 397, 401
Offset: 1

Views

Author

Clark Kimberling, Aug 23 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A010466, A194368, A194381, A194382, A194383.

Programs

  • Mathematica
    r = Sqrt[8]; 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]]   (* A194381 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]   (* A194382 *)
%/2  (* A194383 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 600}];
Flatten[Position[t3, 1]]   (* A194384 *)

A194401 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) < 0, where r=(1+sqrt(5))/2 and < > denotes fractional part.

Original entry on oeis.org

1, 3, 9, 11, 17, 19, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 35, 37, 43, 45, 51, 53, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66, 67, 69, 71, 77, 79, 85, 87, 111, 113, 119, 121, 145, 147, 153, 155, 161, 163, 165, 166, 167, 168, 169, 171, 173, 174, 175, 176, 177
Offset: 1

Views

Author

Clark Kimberling, Aug 24 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A001622, A194368, A194402, A194403, A194404.

Programs

  • Mathematica
    r = GoldenRatio; 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]]       (* A194401 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]       (* A194402 *)
%/2       (* A194403 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]       (* A194404 *)

A194403 (A194402)/2.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 66, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 85, 86, 89
Offset: 1

Views

Author

Clark Kimberling, Aug 24 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A194368.

Programs

  • Mathematica
    r = GoldenRatio; 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]]       (* A194401 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]       (* A194402 *)
%/2                            (* A194403 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]       (* A194404 *)

A194404 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=(1+sqrt(5))/2 and < > denotes fractional part.

Original entry on oeis.org

5, 7, 13, 15, 39, 41, 47, 49, 73, 75, 81, 83, 89, 91, 93, 94, 95, 96, 97, 99, 101, 102, 103, 104, 105, 107, 109, 115, 117, 123, 125, 127, 128, 129, 130, 131, 133, 135, 136, 137, 138, 139, 141, 143, 149, 151, 157, 159, 183, 185, 191, 193, 217, 219, 225
Offset: 1

Views

Author

Clark Kimberling, Aug 24 2011

Keywords

Comments

See A194368.

Crossrefs

Cf. A001622, A194368, A194401, A194402, A194403.

Programs

  • Mathematica
    r = GoldenRatio; 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]]       (* A194401 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]       (* A194402 *)
%/2       (* A194403 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]       (* A194404 *)

A194411 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - ) < 0, where r=sqrt(2) and < > denotes fractional part.

Original entry on oeis.org

2, 14, 26, 38, 41, 43, 44, 50, 53, 55, 56, 62, 65, 67, 68, 70, 71, 72, 73, 74, 77, 79, 80, 82, 83, 84, 85, 86, 89, 91, 92, 94, 95, 96, 97, 98, 101, 113, 125, 137, 140, 142, 143, 149, 152, 154, 155, 161, 164, 166, 167, 212, 224, 236, 239, 241, 242, 248, 251
Offset: 1

Views

Author

Clark Kimberling, Aug 24 2011

Keywords

Comments

See A194368.

Links

Crossrefs

Cf. A002193, A194368, A194412, A194413, A194414.

Programs

  • Mathematica
    r = Sqrt[2]; c = 1/3;
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, 200}];
Flatten[Position[t1, 1]]         (* A194411 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t2, 1]]         (* A194412 *)
%/3                              (* A194413 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 150}];
Flatten[Position[t3, 1]]         (* A194414 *)
Showing 1-10 of 67 results. Next

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

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