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.

User: Norman Carey

Norman Carey's wiki page.

Norman Carey has authored 4 sequences.

A239507 The Lambda word generated by E-1 (A091131).

Original entry on oeis.org

0, 1, 2, 1, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 2, 4, 2, 2, 4, 5, 4, 2, 2, 4, 5, 4, 2, 4, 5, 4, 5, 4, 2, 4, 5, 4, 5, 4, 4, 5, 4, 5, 4, 5, 4, 4, 5, 4, 5, 4, 5, 6, 5, 4, 5, 4, 5, 4, 5, 6, 5, 4, 5, 4, 5, 6, 5, 5, 6, 5, 4, 5, 4, 5, 6, 5, 5, 6, 5, 4, 5, 6, 5, 5, 6, 5, 5, 6, 5, 4, 5, 6, 5, 5, 6, 5, 5, 6, 5, 6, 5, 5, 6, 5, 5, 6, 5, 5, 6, 5, 6, 5
Offset: 0

Views

Author

Norman Carey and Robert G. Wilson v, Mar 20 2014

Keywords

Comments

A Lambda word is a symbolic sequence that encodes differences in the sequence i+j*t, where t is irrational, 1 < t < 2.
First occurrence of k>0: 1, 2, 5, 11, 19, 51, 119, 303, 571, 923, 1359, 4427, 10544, ..., .

Links

Crossrefs

Cf. A216448, A216763, A216764.

Programs

  • Mathematica
    t = E - 1; mx = 20; x = Table[ Ceiling[n*1/t], {n, 0, mx}]; y = Table[ Ceiling[n*t], {n, 0, mx}]; tot[p_, q_] := Total[ Take[x, p + 1]] + (p*q) + Total[ Take[y, q + 1]]; row[r_] := Table[ tot[n, r], {n, 0, mx - 1}]; g = Grid[ Table[ row[n], {n, 0, IntegerPart[(mx - 1)/t]}]]; pos[n_] := Reverse[ Position[ g, n][[1, Range[2, 3]]] - 1]; d[n_] := (d[0] = 0; op[m_] := pos[m + 1] - pos[m]; Abs[ Total[ ContinuedFraction[ op[n][[1]] / op[n][[2]] ]]]); lst = Prepend[ Table[ d[n], {n, 0, 249}], 0]

A216764 The Lambda word generated by Pi - 2.

Original entry on oeis.org

0, 1, 2, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 9, 8, 1, 1, 1, 1, 1, 1, 8, 9, 8, 9, 8, 1, 1, 1, 1, 1, 8, 9, 8, 9, 8, 9, 8, 1, 1, 1, 1, 8, 9, 8, 9, 8, 9, 8, 9, 8, 1, 1, 1, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 1, 1
Offset: 0

Views

Author

Norman Carey, Sep 15 2012

Keywords

Comments

A Lambda word is a symbolic sequence that encodes differences in the sequence i+j*t, where t is irrational, 1 < t < 2. Here, t = Pi - 2.
A Lambda word is an infinite rich word on an infinite alphabet.
First occurrence of k>0: 2, 3, 6, 10, 15, 21, 28, 36, 45, 144, 299, 510, 777, 1100, 1479, ..., . - Robert G. Wilson v, Feb 25 2017

Links

Crossrefs

Cf. A216763 (lambda word generated by (1+sqrt(5))/2), A216448 (lambda word generated by log(3)/log(2)).

Programs

  • Mathematica
    t = Pi - 2;
end = 100;
x = Table[Ceiling[n*1/t], {n, 0, end}];
y = Table[Ceiling[n*t], {n, 0, end}];
tot[p_, q_] := Total[Take[x, p + 1]] + (p*q) + Total[Take[y, q + 1]]
row[r_] := Table[tot[n, r], {n, 0, end - 1}]
g = Grid[Table[row[n], {n, 0, IntegerPart[(end - 1)/t]}]];
pos[n_] := Reverse[Position[g, n][[1, Range[2, 3]]] - 1]
d[n_] := (op[m_] := pos[m + 1] - pos[m];
  Abs[Total[ContinuedFraction[op[n][[1]]/op[n][[2]]]]])
l = Prepend[Table[d[n], {n, 1, 249}], 0]
(* Norman Carey, Sep 16 2012 *)

A216763 The Lambda word generated by (1+sqrt(5))/2.

Original entry on oeis.org

0, 1, 2, 1, 2, 3, 2, 2, 3, 2, 3, 4, 3, 2, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 5, 4, 3, 4, 3, 4, 5, 4, 3, 4, 5, 4, 4, 5, 4, 3, 4, 5, 4, 4, 5, 4, 5, 4, 4, 5, 4, 4, 5, 4, 5, 4, 4, 5, 4, 5, 6, 5, 4, 5, 4, 4, 5, 4, 5, 6, 5, 4, 5, 4, 5, 6, 5, 4, 5, 6, 5, 4, 5, 4, 5, 6, 5, 4, 5, 6, 5, 5, 6, 5, 4, 5, 6
Offset: 0

Views

Author

Norman Carey, Sep 15 2012

Keywords

Comments

A Lambda word is a symbolic sequence that encodes differences in the sequence i+j*t, where t is irrational, 1 < t < 2. This is the Fibonacci Lambda word, t = (1+sqrt(5))/2. The word is achieved by connecting the position numbers of the integers in order from a transpose of the array form of A216448 (0,0), (1,0), (0,1), (2,0), (1,1), and then encoding the vectors starting with (1,0) -> 0, (-1,1) -> 1, (2,-1) -> 2, (-1,1) -> 1.
A Lambda word is a right infinite rich word on an infinite alphabet.

Links

Crossrefs

Cf. A216448, A216764.

Programs

  • Mathematica
    t = GoldenRatio;
end = 100;
x = Table[Ceiling[n*1/t], {n, 0, end}];
y = Table[Ceiling[n*t], {n, 0, end}];
tot[p_, q_] := Total[Take[x, p + 1]] + (p*q) + Total[Take[y, q + 1]]
row[r_] := Table[tot[n, r], {n, 0, end - 1}]
g = Grid[Table[row[n], {n, 0, IntegerPart[(end - 1)/t]}]];
pos[n_] := Reverse[Position[g, n][[1, Range[2, 3]]] - 1]
d[n_] := (op[m_] := pos[m + 1] - pos[m];
  Abs[Total[ContinuedFraction[op[n][[1]]/op[n][[2]]]]])
l = Prepend[Table[d[n], {n, 1, 249}], 0]
(* Norman Carey, Sep 15 2012 *)

A216448 The Lambda word generated by log(3)/log(2).

Original entry on oeis.org

0, 1, 2, 1, 2, 3, 2, 2, 3, 2, 3, 4, 3, 2, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 3, 5, 3, 3, 4, 3, 3, 5, 3, 3, 3, 5, 3, 3, 5, 3, 3, 3, 5, 3, 3, 5, 6, 5, 3, 3, 5, 3, 3, 5, 6, 5, 3, 3, 5, 6, 5, 3, 5, 6, 5, 3, 3, 5, 6, 5, 3, 5, 6, 5, 6, 5, 3, 5, 6, 5, 3, 5, 6, 5, 6, 5, 3, 5, 6, 5, 6, 5, 5, 6, 5, 6, 5, 3, 5, 6, 5, 6, 5, 5, 6
Offset: 0

Views

Author

Norman Carey, Sep 10 2012

Keywords

Comments

A Lambda word is a symbolic sequence that encodes differences in the sequence i+jt, where t is irrational, 1 < t < 2.

Links

Crossrefs

Cf. A003586, A216763, A216764.

Programs

  • Mathematica
    t = Log[2, 3];
end = 100;
x = Table[Ceiling[n*1/t], {n, 0, end }];
y = Table[Ceiling[n*t], {n, 0, end}];
tot[p_, q_] := Total[Take[x, p + 1]] + (p*q) + Total[Take[y, q + 1]]
row[r_] := Table[tot[n, r], {n, 0, end - 1}]
g = Grid[Table[row[n], {n, 0, IntegerPart[(end - 1)/t]}]];
pos[n_] := Reverse[Position[g, n][[1, Range[2, 3]]] - 1]
d[n_] := (d[0] = 0; op[m_] := pos[m + 1] - pos[m];
  Abs[Total[ContinuedFraction[op[n][[1]]/op[n][[2]]] ] ])
l = Prepend[Table[d[n], {n, 1, 249}], 0]
(* Norman Carey, Sep 10 2012 *)

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