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.

A325597 a(n) is the least number not 2a(m) + a(m-1) for any m < n.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 9, 10, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 39, 40, 42, 43, 45, 46, 47, 48, 50, 51, 52, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 69, 70, 72, 73, 74, 75, 77, 78, 79, 81, 82, 84, 85, 86, 87
Offset: 1

Views

Author

Clark Kimberling, May 10 2019

Keywords

Comments

Conjectures: Let d(n) = 3a(n) - 4n; then d(n) is bounded, and d(n) = 0 for infinitely many n.

Examples

			Necessarily, a(1) = 1 and a(2) = 2.  Because of these values, 5 is the least number not in the sequence, so that a(3) = 3 and a(4) = 4.  Consequently, 8 and 11 are disallowed, so a(5) = 6 and a(6) = 7.

Links

Crossrefs

Cf. A325598, A325599, A325417.

Programs

  • Mathematica
    mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]); a = {1}; Do[AppendTo[a, mex[Rest[2 a] + Most[a], Last[a] + 1]], {60}]; a  (* A325597 *)
c = Complement[Range[Last[a]], a]  (* A325598 *)
da = Differences[a] (* A325599 *)
Flatten[Position[da, 1]]  (* A325600 *)
Flatten[Position[da, 2]]  (* A325601 *)
(* Peter J. C. Moses, May 07 2019 *)

A325598 Complement of A325597.

Original entry on oeis.org

5, 8, 11, 16, 20, 25, 29, 34, 38, 41, 44, 49, 53, 56, 61, 65, 68, 71, 76, 80, 83, 88, 92, 95, 98, 103, 107, 110, 115, 119, 124, 128, 133, 137, 140, 143, 148, 152, 155, 160, 164, 169, 173, 176, 179, 184, 188, 191, 196, 200, 205, 209, 214, 218, 221, 224, 229
Offset: 1

Views

Author

Clark Kimberling, May 10 2019

Keywords

Comments

These are the numbers 2a(m) + a(m-1) for a(m)=A325597(m), m >= 1 .

Links

Crossrefs

Cf. A325597.

Programs

  • Mathematica
    mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]); a = {1}; Do[AppendTo[a, mex[Rest[2 a] + Most[a], Last[a] + 1]], {60}]; a  (* A325597 *)
c = Complement[Range[Last[a]], a]  (* A325598 *)
da = Differences[a] (* A325599 *)
Flatten[Position[da, 1]] (* A325600 *)
Flatten[Position[da, 2]] (* A325601 *)
(* Peter J. C. Moses, May 07 2019 *)

A325599 Difference sequence of A325597.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2
Offset: 1

Views

Author

Clark Kimberling, May 11 2019

Keywords

Comments

All the terms of A325599 are in {1,2}, so that A325600 and A325601 are a complementary pair.

Links

Crossrefs

Cf. A325597.

Programs

  • Mathematica
    mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]); a = {1}; Do[AppendTo[a, mex[Rest[2 a] + Most[a], Last[a] + 1]], {60}]; a  (* A325597 *)
c = Complement[Range[Last[a]], a]  (* A325598 *)
da = Differences[a] (* A325599 *)
Flatten[Position[da, 1]]  (* A325600 *)
Flatten[Position[da, 2]]  (* A325601 *)
(* Peter J. C. Moses, May 07 2019 *)

A325601 Positions of 2 in A325599.

Original entry on oeis.org

4, 6, 8, 12, 15, 19, 22, 26, 29, 31, 33, 37, 40, 42, 46, 49, 51, 53, 57, 60, 62, 66, 69, 71, 73, 77, 80, 82, 86, 89, 93, 96, 100, 103, 105, 107, 111, 114, 116, 120, 123, 127, 130, 132, 134, 138, 141, 143, 147, 150, 154, 157, 161, 164, 166, 168, 172, 175, 177
Offset: 1

Views

Author

Clark Kimberling, May 11 2019

Keywords

Comments

All the terms of A325599 are in {1,2}, so that A325600 and A325601 are a complementary pair.

Links

Crossrefs

Cf. A325597, A325599, A325600.

Programs

  • Mathematica
    mex[list_, start_] := (NestWhile[# + 1 &, start, MemberQ[list, #] &]); a = {1}; Do[AppendTo[a, mex[Rest[2 a] + Most[a], Last[a] + 1]], {60}]; a  (* A325597 *)
c = Complement[Range[Last[a]], a]  (* A325598 *)
da = Differences[a] (* A325599 *)
Flatten[Position[da, 1]]  (* A325600 *)
Flatten[Position[da, 2]]  (* A325601 *)
(* Peter J. C. Moses, May 07 2019 *)
Showing 1-4 of 4 results.

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