A133299 -id:A133299 - cp's OEIS frontend

A191433 Dispersion of ([n*x+n+1/2]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

1, 3, 2, 8, 5, 4, 21, 13, 10, 6, 55, 34, 26, 16, 7, 144, 89, 68, 42, 18, 9, 377, 233, 178, 110, 47, 24, 11, 987, 610, 466, 288, 123, 63, 29, 12, 2584, 1597, 1220, 754, 322, 165, 76, 31, 14, 6765, 4181, 3194, 1974, 843, 432, 199, 81, 37, 15, 17711, 10946

Offset: 1

Clark Kimberling, Jun 03 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1....3....8....21...55...144
  2....5....13...34...89...233
  4....10...26...68...178..466
  6....16...42...110..288..754
  7....18...47...123..322..843

Cf. A114537, A035513, A035506.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r = 40; r1 = 12;  (* r=# rows of T, r1=# rows to show *)
c = 40; c1 = 12;  (* c=# cols of T, c1=# cols to show *)
x = 1 + GoldenRatio;
f[n_] := Floor[n*x + 1/2] (* f(n) is complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1,
  Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]] (* A191433 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191433 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191434 Dispersion of ([n*x+n+3/2]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 4, 2, 11, 6, 3, 30, 17, 9, 5, 80, 46, 25, 14, 7, 210, 121, 66, 38, 19, 8, 551, 318, 174, 100, 51, 22, 10, 1444, 834, 457, 263, 135, 59, 27, 12, 3781, 2184, 1197, 690, 354, 155, 72, 32, 13, 9900, 5719, 3135, 1807, 928, 407, 189, 85, 35, 15, 25920, 14974

Offset: 1

Clark Kimberling, Jun 04 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1.....4....11....30...80
  2.....6....17....46...121
  3.....9....25....66...174
  5.....14...38...100...263
  7.....19...51...135...354

Cf. A114537, A035513, A035506, A191426.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r = 40; r1 = 12; c = 40; c1 = 12;
x = 1 + GoldenRatio; f[n_] := Floor[n*x + 3/2]
(* f(n) is complement of column 1 *)
mex[list_] :=  NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1,
  Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191434 array *)
Flatten[Table[
  t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]]
(* A191434 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191435 Dispersion of ([n*x+n+x]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 5, 2, 15, 7, 3, 41, 20, 10, 4, 109, 54, 28, 13, 6, 287, 143, 75, 36, 18, 8, 753, 376, 198, 96, 49, 23, 9, 1973, 986, 520, 253, 130, 62, 26, 11, 5167, 2583, 1363, 664, 342, 164, 70, 31, 12, 13529, 6764, 3570, 1740, 897, 431, 185, 83, 34, 14, 35421, 17710

Offset: 1

Clark Kimberling, Jun 04 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1....5....15...41...109
  2....7....20...54...143
  3....10...28...75...198
  4....13...36...96...253
  6....18...49...130..342

Cf. A114537, A035513, A035506.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r = 40; r1 = 12;  c = 40; c1 = 12;  x = 1 + GoldenRatio;
f[n_] := Floor[n*x + x] (* f(n),complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191435 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191435 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191437 Dispersion of ([n*x+n+x-2]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 3, 2, 8, 5, 4, 21, 13, 11, 6, 55, 34, 29, 16, 7, 144, 89, 76, 42, 18, 9, 377, 233, 199, 110, 47, 24, 10, 987, 610, 521, 288, 123, 63, 26, 12, 2584, 1597, 1364, 754, 322, 165, 68, 32, 14, 6765, 4181, 3571, 1974, 843, 432, 178, 84, 37, 15, 17711, 10946

Offset: 1

Clark Kimberling, Jun 04 2011

Rows 1 and 2:  Fibonacci numbers.  Rows 3 and 5: Lucas numbers.  Row n satisfies the recurrence x(n)=3*x(n-1)-x(n-2).
Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1....3....8....21...55
  2....5....13...34...89
  4....11...29...76...199
  6....16...42...110..288
  7....18...47...123..322

Cf. A114537, A035513, A035506, A000045, A000032, A191426.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r = 40; r1 = 12;  c = 40; c1 = 12;  x = GoldenRatio;
f[n_] := Floor[n*x+n+x-2] (* complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191437 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191437 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191440 Dispersion of ([n*sqrt(2)+n+3/2]), where [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 3, 2, 8, 6, 4, 20, 15, 11, 5, 49, 37, 28, 13, 7, 119, 90, 69, 32, 18, 9, 288, 218, 168, 78, 44, 23, 10, 696, 527, 407, 189, 107, 57, 25, 12, 1681, 1273, 984, 457, 259, 139, 61, 30, 14, 4059, 3074, 2377, 1104, 626, 337, 148, 73, 35, 16, 9800, 7422, 5740

Offset: 1

Clark Kimberling, Jun 04 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1....3....8....20...49
  2....6....15...37...90
  4....11...28...69...168
  5....13...32...78...189
  7....18...44...107..259

Cf. A114537, A035513, A035506, A191438, A191439, A083087.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r=40; r1=12; c=40; c1=12;  x = Sqr[2];
f[n_] := Floor[n*x+n+3/2] (* complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191440 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191440 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191441 Dispersion of ([n*x+n+x]), where x=sqrt(2) and [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 4, 2, 12, 7, 3, 31, 19, 9, 5, 77, 48, 24, 14, 6, 188, 118, 60, 36, 16, 8, 456, 287, 147, 89, 41, 21, 10, 1103, 695, 357, 217, 101, 53, 26, 11, 2665, 1680, 864, 526, 246, 130, 65, 28, 13, 6436, 4058, 2088, 1272, 596, 316, 159, 70, 33, 15, 15540, 9799, 5043

Offset: 1

Clark Kimberling, Jun 04 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1....4....12...31...77
  2....7....19...48...118
  3....9....24...60...147
  5....14...36...89...217
  6....16...41...101..246

Cf. A114537, A035513, A035506, A191438.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r=40; r1=12; c=40; c1=12;  x = Sqr[2];
f[n_] := Floor[n*x+n+x] (* complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191441 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191441 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191443 Dispersion of the sequence ([n*sqrt(3)+1]), where [ ]=floor, read by antidiagonals.

Original entry on oeis.org

1, 2, 3, 4, 6, 5, 7, 11, 9, 8, 13, 20, 16, 14, 10, 23, 35, 28, 25, 18, 12, 40, 61, 49, 44, 32, 21, 15, 70, 106, 85, 77, 56, 37, 26, 17, 122, 184, 148, 134, 97, 65, 46, 30, 19, 212, 319, 257, 233, 169, 113, 80, 52, 33, 22, 368, 553, 446, 404, 293, 196, 139

Offset: 1

Clark Kimberling, Jun 04 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1....2....4....7....13
  3....6....11...20...35
  5....9....16...28...49
  8....14...25...44...77
  10...18...32...56...97

Cf. A114537, A035513, A035506, A191442.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r=40; r1=12; c=40; c1=12;  x = Sqrt[3];
f[n_] := Floor[n*x+1] (* complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191443 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191443 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191444 Dispersion of ([n*sqrt(3)+3/2]), where [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 3, 2, 6, 4, 5, 11, 8, 10, 7, 20, 15, 18, 13, 9, 36, 27, 32, 24, 17, 12, 63, 48, 56, 43, 30, 22, 14, 110, 84, 98, 75, 53, 39, 25, 16, 192, 146, 171, 131, 93, 69, 44, 29, 19, 334, 254, 297, 228, 162, 121, 77, 51, 34, 21, 580, 441, 515, 396, 282, 211, 134

Offset: 1

Clark Kimberling, Jun 04 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1....3....6....11...20
  2....4....8....15...27
  5....10...18...32...56
  7....13...24...43...75
  9....17...30...53...93

Cf. A114537, A035513, A035506, A191442.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r=40; r1=12; c=40; c1=12;  x = Sqr[3];
f[n_] := Floor[n*x+3/2] (* complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191444 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191444 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191445 Dispersion of ([(n+1)*sqrt(3)]), where [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 3, 2, 6, 5, 4, 12, 10, 8, 7, 22, 19, 15, 13, 9, 39, 34, 27, 24, 17, 11, 69, 60, 48, 43, 31, 20, 14, 121, 105, 84, 76, 55, 36, 25, 16, 211, 183, 147, 133, 96, 64, 45, 29, 18, 367, 318, 256, 232, 168, 112, 79, 51, 32, 21, 637, 552, 445, 403, 292, 195, 138

Offset: 1

Clark Kimberling, Jun 04 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1...3...6...12..22
  2...5...10..19..34
  4...8...15..27..48
  7...13..24..43..76
  9...17..31..55..96

Cf. A114537, A035513, A035506, A191442.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r=40; r1=12; c=40; c1=12;  x = Sqr[3];
f[n_] := Floor[n*x+x] (* complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191445 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191445 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

A191447 Dispersion of (1+[n*sqrt(5)]), where [ ]=floor, by antidiagonals.

Original entry on oeis.org

1, 3, 2, 7, 5, 4, 16, 12, 9, 6, 36, 27, 21, 14, 8, 81, 61, 47, 32, 18, 10, 182, 137, 106, 72, 41, 23, 11, 407, 307, 238, 161, 92, 52, 25, 13, 911, 687, 533, 361, 206, 117, 56, 30, 15, 2038, 1537, 1192, 808, 461, 262, 126, 68, 34, 17, 4558, 3437, 2666, 1807

Offset: 1

Clark Kimberling, Jun 05 2011

Background discussion:  Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1.  The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...).  Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers.  The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence.  Examples:
(1) s=A000040 (the primes), D=A114537, u=A114538.
(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.
(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.
More recent examples of dispersions: A191426-A191455.

			Northwest corner:
  1...3....7....16...36
  2...5....12...27...61
  4...9....21...47...106
  6...14...32...72...161
  8...18...41...92...206

Cf. A114537, A035513, A035506, A191446.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r=40; r1=12; c=40; c1=12;  x = Sqrt[5];
f[n_] := 1+Floor[n*x] (* complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191447 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191447 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

cp's OEIS Frontend

A191433 Dispersion of ([n*x+n+1/2]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

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A191434 Dispersion of ([n*x+n+3/2]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

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Mathematica

A191435 Dispersion of ([n*x+n+x]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

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A191437 Dispersion of ([n*x+n+x-2]), where x=(golden ratio) and [ ]=floor, by antidiagonals.

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A191440 Dispersion of ([n*sqrt(2)+n+3/2]), where [ ]=floor, by antidiagonals.

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A191441 Dispersion of ([n*x+n+x]), where x=sqrt(2) and [ ]=floor, by antidiagonals.

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A191443 Dispersion of the sequence ([n*sqrt(3)+1]), where [ ]=floor, read by antidiagonals.

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A191444 Dispersion of ([n*sqrt(3)+3/2]), where [ ]=floor, by antidiagonals.

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A191445 Dispersion of ([(n+1)*sqrt(3)]), where [ ]=floor, by antidiagonals.

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