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 1-4 of 4 results.

A192646 First differences of A192645.

Original entry on oeis.org

1, 1, 2, 3, 8, 5, 3, 15, 16, 5, 3, 72, 50, 7, 39, 16, 5, 3, 65, 49, 8, 39, 16, 5, 3, 72, 39, 16, 5, 3, 369, 1, 135, 185, 192, 39, 8, 8, 5, 3, 1, 368, 190, 369, 1, 46, 89, 47, 8, 130, 192, 39, 16, 5, 3, 17, 118, 185, 49, 48, 87, 8, 39, 16, 5, 3, 114, 192, 39, 16, 5, 3, 48
Offset: 1

Views

Author

Clark Kimberling, Jul 06 2011

Keywords

Comments

Does this sequence include 1 infinitely many times?

Examples

			A192645 = (1, 2, 3, 5, 8, 16, 21, ...) gives (2-1, 3-2, 5-3, 8-5, 16-8, 21-16, ...)

Crossrefs

Cf. A192476, A192645.

Programs

  • Mathematica
    start = {1, 2};
f[x_, y_] := If[MemberQ[Range[1, 5000], x^2 - y^2], x^2 - y^2]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      5000 &]];
t = FixedPoint[b, start]  (* A192645 *)
Differences[t] (* A192646 *)

A192649 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2-y^2>0 then x^2-y^2 is in S, and 1, 2, and 4 are in S.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 12, 15, 16, 17, 21, 24, 31, 32, 33, 39, 40, 45, 48, 55, 56, 60, 63, 64, 65, 72, 77, 79, 80, 81, 95, 111, 112, 119, 127, 128, 129, 135, 140, 143, 144, 145, 152, 159, 161, 175, 176, 185, 192, 200, 207, 208, 209, 216, 221, 223, 224, 225, 231
Offset: 1

Views

Author

Clark Kimberling, Jul 06 2011

Keywords

Comments

See A192645.

Links

Crossrefs

Cf. A192476, A192646, A192650.

Programs

  • Mathematica
    start = {1, 2, 4};
f[x_, y_] := If[MemberQ[Range[1, 700], x^2 - y^2], x^2 - y^2]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      700 &]];
t = FixedPoint[b, start]  (* A192649 *)
Differences[t] (* A192650 *)

A192647 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2 - y^2 > 0 then x^2 - y^2 is in S, and 1 and 3 are in S.

Original entry on oeis.org

1, 3, 8, 55, 63, 944, 2961, 3016, 3024, 3905, 3960, 3968, 48320, 63424, 328735, 377055, 432575, 495999, 887167, 888111, 891072, 891127, 891135, 6104449, 6152769, 6481504, 6537024, 6585344, 6600448, 6648768, 6914079, 6977503, 7876385, 8205120
Offset: 1

Views

Author

Clark Kimberling, Jul 06 2011

Keywords

Comments

See A192645.

Links

Crossrefs

Cf. A192476, A192646.

Programs

  • Mathematica
    start = {1, 3};
f[x_, y_] := If[MemberQ[Range[1, 500000], x^2 - y^2], x^2 - y^2]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      500000 &]];
t = FixedPoint[b, start]  (* A192647 *)

A192648 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2-y^2>0 then x^2-y^2 is in S, and 2 and 3 are in S.

Original entry on oeis.org

2, 3, 5, 16, 21, 185, 231, 247, 252, 416, 432, 437, 2495, 4345, 7648, 10143, 13568, 17913, 19136, 26784, 29279, 33784, 33969, 34200, 34216, 34221, 52920, 53105, 53336, 53352, 53357, 60568, 60753, 60984, 61000, 61005, 63063, 63248, 63479
Offset: 1

Views

Author

Clark Kimberling, Jul 06 2011

Keywords

Comments

See A192645.

Links

Crossrefs

Cf. A192476, A192646.

Programs

  • Mathematica
    start = {2, 3};
f[x_, y_] := If[MemberQ[Range[1, 150000], x^2 - y^2], x^2 - y^2]
b[x_] :=
  Block[{w = x},
   Select[Union[
     Flatten[AppendTo[w,
       Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # <
      150000 &]];
t = FixedPoint[b, start]  (* A192648 *)
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.