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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A325497 Difference sequence of A325422.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 05 2019

Keywords

Comments

See A325417 for a guide to related sequences. Conjecture: every term is in {1,2,3,4,6}.

Examples

			A325422 is given by A(n) = least number not 2*A(m)+1 or 3*A(m)+1 for any m < n, so that A = (3,4,5,7,13,17,19,...), with differences (1,1,2,6,4,2,...).

Links

Crossrefs

Cf. A325417, A325422.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{(#-1)/3, (# - 1)/2}],
IntegerQ]]] &]], {2000}]; a ;       (* A077477 *)
c = Complement[Range[Last[a]], a] ; (* A325422 *)
Differences[a]  (* A325496 *)
Differences[c]  (* A325497 *)
(* Peter J. C. Moses, Apr 23 2019 *)

A325499 Difference sequence of A325424.

Original entry on oeis.org

1, 5, 2, 2, 2, 1, 3, 3, 1, 4, 1, 5, 1, 1, 4, 1, 1, 6, 2, 2, 1, 5, 1, 1, 2, 2, 7, 1, 2, 2, 1, 7, 2, 2, 1, 1, 2, 3, 1, 4, 6, 1, 1, 2, 2, 1, 7, 4, 1, 3, 2, 1, 1, 2, 2, 1, 1, 5, 1, 4, 1, 5, 2, 2, 2, 1, 1, 2, 3, 1, 4, 7, 1, 4, 1, 1, 5, 1, 2, 2, 1, 3, 2, 1, 1, 2
Offset: 1

Views

Author

Clark Kimberling, May 05 2019

Keywords

Comments

See A325417 for a guide to related sequences.
Conjecture: every term is in {1,2,3,4,5,6,7}.

Links

Crossrefs

Cf. A325424, A325417, A036668, A325498.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/3, #/2}],
IntegerQ]]] &]], {2000}]; a ;       (* A036668 *)
c = Complement[Range[Last[a]], a] ; (* A325424 *)
Differences[a]  (* A325498 *)
Differences[c]  (* A325499 *)
(* Peter J. C. Moses, Apr 23 2019 *)

Formula

Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} a(k) = 12/5. - Amiram Eldar, Nov 26 2020

A325518 Difference sequence of A325425.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 06 2019

Keywords

Comments

See A325417 for a guide to related sequences. Conjecture: every term is in {1,2,3,4,5,6}.

Links

Crossrefs

Cf. A325417, A325425, A325519.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{#/2,
If[Mod[#, 3] == 0, (2 #)/3, 0] + If[Mod[#, 3] == 1, 1/3 (1 + 2 #), 0]}],
IntegerQ || # == 0]]] &]], {200}]; a ; (* A325425 *)
c = Complement[Range[Last[a]], a] ;    (* A325426 *)
Differences[a]  (* A325518 *)
Differences[c]  (* A325519 *)
(* Peter J. C. Moses, Apr 23 2019 *)

A325519 Difference sequence of A325426.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 06 2019

Keywords

Comments

See A325417 for a guide to related sequences. Conjecture: every term is in {1,2,3,4,5,6,7}.

Links

Crossrefs

Cf. A325417, A325426, A325518.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{#/2,
If[Mod[#, 3] == 0, (2 #)/3, 0] + If[Mod[#, 3] == 1, 1/3 (1 + 2 #), 0]}],
IntegerQ || # == 0]]] &]], {200}]; a ; (* A325425 *)
c = Complement[Range[Last[a]], a] ;    (* A325426 *)
Differences[a]  (* A325518 *)
Differences[c]  (* A325519 *)
(* Peter J. C. Moses, Apr 23 2019 *)

A325520 Difference sequence of A325427.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 06 2019

Keywords

Comments

See A325417 for a guide to related sequences. Conjecture: every term is in {1,2,3,4,5,6}.

Links

Crossrefs

Cf. A325417, A325427, A325521.

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]]] &]], {200}]; a ; (* A325427 *)
c = Complement[Range[Last[a]], a] ;    (* A325428 *)
Differences[a]  (* A325520 *)
Differences[c]  (* A325521 *)
(* Peter J. C. Moses, Apr 23 2019 *)

A325521 Difference sequence of A325428.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 06 2019

Keywords

Examples

			See A325417 for a guide to related sequences. Conjecture: every term is in {1,2,3,4,5,6,7,8,9}.

Links

Crossrefs

Cf. A325417, A325428, A325520.

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]]] &]], {200}]; a ; (* A325427 *)
c = Complement[Range[Last[a]], a] ;    (* A325428 *)
Differences[a]  (* A325520 *)
Differences[c]  (* A325521 *)
(* Peter J. C. Moses, Apr 23 2019 *)

A325522 Difference sequence of A325429.

Original entry on oeis.org

1, 2, 1, 3, 1, 1, 1, 3, 3, 1, 1, 1, 2, 1, 3, 3, 2, 1, 3, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 3, 3, 2, 1, 3, 1, 1, 1, 3, 3, 1, 2, 2, 1, 3, 1, 1, 1, 2, 1, 3, 1, 1, 1, 3, 3, 1, 1, 1, 2, 1, 3, 2, 1, 2, 1, 3, 1, 1, 1, 3, 3, 1, 2, 2, 1, 3, 3, 2, 1, 3, 1, 1, 1, 3, 3, 1
Offset: 1

Views

Author

Clark Kimberling, May 06 2019

Keywords

Comments

See A325417 for a guide to related sequences. Conjecture: every term is in {1,2,3}.

Links

Crossrefs

Cf. A325417, A325429, A325523.

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]]] &]], {20000}]; a ;   (* A325429 *)
c = Complement[Range[Last[a]], a] ;        (* A325430 *)
Differences[a]  (* A325522 *)
Differences[c]  (* A325523 *)
(* Peter J. C. Moses, Apr 23 2019 *)

A325523 Difference sequence of A325430.

Original entry on oeis.org

3, 1, 5, 1, 2, 1, 5, 3, 1, 2, 1, 2, 3, 1, 5, 3, 1, 3, 2, 3, 1, 2, 1, 2, 3, 1, 5, 1, 2, 1, 3, 2, 3, 1, 5, 3, 1, 5, 1, 2, 1, 5, 3, 1, 2, 3, 3, 1, 5, 1, 2, 1, 3, 2, 3, 1, 2, 1, 2, 3, 1, 5, 1, 2, 1, 3, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 1, 5, 3, 1, 2, 3, 3, 1, 5, 3
Offset: 1

Views

Author

Clark Kimberling, May 06 2019

Keywords

Comments

See A325417 for a guide to related sequences. Conjecture: every term is in {1,2,3,5}.

Links

Crossrefs

Cf. A325417, A325430, A325522.

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]]] &]], {20000}]; a ;   (* A325429 *)
c = Complement[Range[Last[a]], a] ;        (* A325430 *)
Differences[a]  (* A325522 *)
Differences[c]  (* A325523 *)
(* Peter J. C. Moses, Apr 23 2019 *)

A325525 Difference sequence of A325432.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, May 06 2019

Keywords

Comments

See A325417 for a guide to related sequences.
Conjecture: every term is in {1,2,3,4,5,6,7,9}; note that 8 is missing.

Links

Crossrefs

Cf. A325417, A325432, A325524.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{#/3, #/4}],
IntegerQ]]] &]], {20000}]; a;         (* A315431 *)
c = Complement[Range[Last[a]], a] ;   (* A325432 *)
Differences[a]  (* A325524 *)
Differences[c]  (* A325525 *)
(* Peter J. C. Moses, Apr 23 2019 *)

Formula

Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} a(k) = 20/7. - Amiram Eldar, Nov 26 2020

A325526 Difference sequence of A325462.

Original entry on oeis.org

2, 1, 1, 2, 2, 3, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 3, 1, 2, 1, 1, 2, 2, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 3, 2, 1, 1, 2, 2, 1, 1, 2, 2, 3, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 3, 1, 2, 1, 1, 2, 2, 4, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2
Offset: 1

Views

Author

Clark Kimberling, May 07 2019

Keywords

Comments

See A325417 for a guide to related sequences. Conjecture: every term is in {1,2,3,4}.

Links

Crossrefs

Cf. A325417, A325426, A325527.

Programs

  • Mathematica
    a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1, Apply[Or,
Map[MemberQ[a, #] &, Select[Flatten[{#/2, (#+1)/3}],
IntegerQ]]] &]], {20000}]; a;         (* A315462 *)
c = Complement[Range[Last[a]], a] ;   (* A325463 *)
Differences[a]  (* A325526 *)
Differences[c]  (* A325527 *)
(* Peter J. C. Moses, Apr 23 2019 *)
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