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.

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A325428 Complement of A325427.

Original entry on oeis.org

3, 5, 6, 9, 10, 12, 15, 16, 17, 19, 21, 23, 27, 29, 30, 33, 36, 37, 39, 41, 42, 45, 46, 48, 49, 51, 52, 53, 57, 60, 63, 64, 65, 66, 69, 70, 71, 75, 77, 81, 82, 84, 87, 88, 89, 91, 93, 95, 100, 101, 102, 108, 109, 111, 113, 114, 117, 118, 119, 120, 123, 124
Offset: 1

Views

Author

Clark Kimberling, Apr 30 2019

Keywords

Comments

These are the numbers 2x+1 and floor(3x/2) as x ranges through the numbers x>1 in A325427.

Links

Crossrefs

Cf. A325417, A325427.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{(#-1)/2,
If[Mod[#, 3] == 0, (2 #)/3, 0] + If[Mod[#, 3] == 1, 1/3 (1 + 2 #), 0]}],
IntegerQ || # == 0]]] &]], {150}]; a  (* A325427 *)
Complement[Range[Last[a]], a]         (* A325428 *)
(* Peter J. C. Moses, Apr 25 2019 *)

A325429 a(n) is the least number not 3*a(m) or floor(3*a(m)/2) for any m < n.

Original entry on oeis.org

1, 2, 4, 5, 8, 9, 10, 11, 14, 17, 18, 19, 20, 22, 23, 26, 29, 31, 32, 35, 36, 37, 38, 40, 41, 44, 45, 47, 49, 50, 53, 56, 58, 59, 62, 63, 64, 65, 68, 71, 72, 74, 76, 77, 80, 81, 82, 83, 85, 86, 89, 90, 91, 92, 95, 98, 99, 100, 101, 103, 104, 107, 109, 110
Offset: 1

Views

Author

Clark Kimberling, Apr 30 2019

Keywords

Examples

			The sequence necessarily starts with 1.  The next 2 terms are determined as follows:  because a(1) = 1, the number 3 is disallowed, so that a(2) = 2, whence the numbers 3 and 6 are disallowed, and a(3) = 4.  See A325417 for a guide to related sequences.

Links

Crossrefs

Cf. A325417, A325430.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{#/3,
If[Mod[#, 3] == 0, (2 #)/3, 0] + If[Mod[#, 3] == 1, 1/3 (1 + 2 #), 0]}],
IntegerQ || # == 0]]] &]], {150}]; a  (* A325429 *)
Complement[Range[Last[a]], a]         (* A325430 *)
(* Peter J. C. Moses, Apr 25 2019 *)

A325430 Complement of A325429.

Original entry on oeis.org

3, 6, 7, 12, 13, 15, 16, 21, 24, 25, 27, 28, 30, 33, 34, 39, 42, 43, 46, 48, 51, 52, 54, 55, 57, 60, 61, 66, 67, 69, 70, 73, 75, 78, 79, 84, 87, 88, 93, 94, 96, 97, 102, 105, 106, 108, 111, 114, 115, 120, 121, 123, 124, 127, 129, 132, 133, 135, 136, 138, 141
Offset: 1

Views

Author

Clark Kimberling, Apr 30 2019

Keywords

Comments

These are the numbers 3x and floor(3x/2) as x ranges through the numbers x>1 in A325429.

Links

Crossrefs

Cf. A325417, A325429.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{#/3,
If[Mod[#, 3] == 0, (2 #)/3, 0] + If[Mod[#, 3] == 1, 1/3 (1 + 2 #), 0]}],
IntegerQ || # == 0]]] &]], {150}]; a  (* A325429 *)
Complement[Range[Last[a]], a]         (* A325430 *)
(* Peter J. C. Moses, Apr 25 2019 *)

A325441 Complement of A325440.

Original entry on oeis.org

2, 5, 7, 8, 11, 17, 19, 23, 25, 26, 27, 29, 31, 35, 38, 39, 41, 43, 44, 47, 53, 55, 59, 62, 63, 65, 67, 71, 73, 79, 83, 89, 91, 95, 97, 98, 99, 101, 103, 107, 110, 111, 113, 115, 119, 121, 125, 127, 131, 134, 135, 137, 139, 143, 146, 147, 149, 151, 152, 153
Offset: 1

Views

Author

Clark Kimberling, May 02 2019

Keywords

Comments

These are the numbers 2x-1 and 3x-1 as x ranges through the numbers x>1 in A325440.

Links

Crossrefs

Cf. A325417, A325440.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{(#+1)/2, (#+1)/3}],
IntegerQ]]] &]], {150}]; a          (* A325440 *)
Complement[Range[Last[a]], a]       (* A325441 *)
(* Peter J. C. Moses, Apr 25 2019 *)

A325443 Complement of A325442.

Original entry on oeis.org

3, 6, 7, 9, 12, 15, 19, 21, 24, 25, 27, 30, 31, 33, 35, 39, 42, 43, 45, 48, 51, 54, 55, 57, 60, 63, 66, 67, 69, 71, 73, 75, 78, 79, 81, 84, 87, 91, 93, 96, 97, 99, 102, 103, 105, 108, 111, 114, 115, 117, 120, 121, 123, 127, 129, 132, 135, 138, 139, 141, 143
Offset: 1

Views

Author

Clark Kimberling, May 02 2019

Keywords

Comments

These are the numbers 2x-1 and 3x as x ranges through the numbers x>1 in A325442.

Links

Crossrefs

Cf. A325417, A325442.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{(#+1)/2, #/3}],
IntegerQ]]] &]], {150}]; a          (* A325442 *)
Complement[Range[Last[a]], a]       (* A325443 *)
(* Peter J. C. Moses, Apr 25 2019 *)

A325463 Complement of A325462.

Original entry on oeis.org

2, 6, 8, 10, 11, 14, 18, 20, 24, 26, 30, 32, 34, 35, 38, 42, 44, 46, 47, 50, 54, 56, 58, 62, 65, 66, 68, 72, 74, 78, 80, 82, 83, 86, 90, 92, 96, 98, 102, 104, 106, 107, 110, 114, 116, 118, 119, 120, 122, 126, 128, 134, 138, 140, 142, 143, 146, 150, 152, 154
Offset: 1

Views

Author

Clark Kimberling, May 01 2019

Keywords

Comments

These are the numbers 2x and 3x-1 as x ranges through the numbers x>1 in A325462.

Links

Crossrefs

Cf. A325417, A325462.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{#/2, (#+1)/3}],
IntegerQ]]] &]], {150}]; a       (* A325462 *)
Complement[Range[Last[a]], a]    (* A325463 *)
(* Peter J. C. Moses, Apr 25 2019 *)

A325465 Complement of A325464.

Original entry on oeis.org

2, 6, 7, 8, 10, 13, 18, 22, 24, 25, 28, 30, 31, 32, 34, 38, 40, 42, 43, 46, 49, 52, 54, 55, 58, 61, 66, 67, 70, 72, 74, 76, 78, 79, 82, 85, 88, 90, 94, 96, 97, 100, 102, 103, 106, 109, 112, 114, 115, 118, 120, 121, 124, 126, 128, 130, 133, 136, 138, 139, 142
Offset: 1

Views

Author

Clark Kimberling, May 01 2019

Keywords

Comments

These are the numbers 2x and 3x-2 as x ranges through the numbers x>1 in A325464.

Links

Crossrefs

Cf. A325417, A325464.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{#/2, (#+2)/3}],
IntegerQ]]] &]], {150}]; a          (* A325464 *)
Complement[Range[Last[a]], a]       (* A325465 *)
(* Peter J. C. Moses, Apr 25 2019 *)

A325539 a(n) is the least number not 2*a(m)+1 or 3*a(m)+2 for any m < n.

Original entry on oeis.org

1, 2, 4, 6, 7, 10, 11, 12, 16, 17, 18, 19, 22, 24, 26, 27, 28, 29, 30, 31, 34, 36, 40, 41, 42, 43, 44, 46, 47, 48, 51, 52, 54, 58, 60, 62, 64, 65, 66, 67, 70, 71, 72, 75, 76, 77, 78, 79, 82, 84, 88, 90, 91, 94, 96, 98, 99, 100, 101, 102, 106, 107, 108, 111
Offset: 1

Views

Author

Clark Kimberling, May 07 2019

Keywords

Examples

			The sequence necessarily starts with 1.  The next 2 terms are determined as follows:  because a(1) = 1, the numbers 3 and 5 are disallowed, so that a(2) = 2, whence the number 8 is disallowed, and a(3) = 4.  See A325417 for a guide to related sequences.

Links

Crossrefs

Cf. A325417, A325540.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &,  Select[Flatten[{(# - 1)/2, (# - 2)/3}],
IntegerQ]]] &]], {200}]; a       (* A325539 *)
Complement[Range[Last[a]], a]    (* A325540 *)
(* Peter J. C. Moses, Apr 25 2019 *)

A325540 Complement of A325539.

Original entry on oeis.org

3, 5, 8, 9, 13, 14, 15, 20, 21, 23, 25, 32, 33, 35, 37, 38, 39, 45, 49, 50, 53, 55, 56, 57, 59, 61, 63, 68, 69, 73, 74, 80, 81, 83, 85, 86, 87, 89, 92, 93, 95, 97, 103, 104, 105, 109, 110, 117, 121, 122, 125, 128, 129, 131, 133, 134, 135, 140, 141, 143, 145
Offset: 1

Views

Author

Clark Kimberling, May 07 2019

Keywords

Comments

These are the numbers 2x+1 and 3x+2 as x ranges through the numbers x > 1 in A325539.

Links

Crossrefs

Cf. A325417, A325539.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &,  Select[Flatten[{(# - 1)/2, (# - 2)/3}],
IntegerQ]]] &]], {200}]; a            (* A325539 *)
Complement[Range[Last[a]], a]    (* A325540 *)
(* Peter J. C. Moses, Apr 25 2019 *)

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 *)
Previous Showing 11-20 of 50 results. Next

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