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 1-8 of 8 results.

A050129 a(n) is the least k satisfying A050128(k) = n.

Original entry on oeis.org

1, 3, 9, 2, 6, 15, 8, 4, 20, 5, 12, 27, 14, 7, 32, 17, 37, 19, 40, 10, 22, 11, 24, 51, 26, 13, 56, 29, 61, 31, 64, 16, 34, 71, 36, 18, 76, 39, 81, 163, 42, 21, 44, 91, 46, 23, 48, 99, 50, 25, 104, 53, 109, 55, 112, 28, 58, 119, 60, 30, 124, 63
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

Conjecture: for n > 1, a(n) is always one of n/2, n+1, 2*n+2, 2*n+3, 4*n+3 or 4*n+5. - Robert Israel, Feb 18 2020

Links

Crossrefs

Cf. A050128.

Programs

  • Maple
    N:= 100: # to get a(1)..a(N)
A[1]:= 1: S:= {0,1}: count:= 1:
v:= 1:
for n from 2 while count < N do
  v:= floor(v/2);
  if member(v, S) then v:= 2*n fi;
  if v <= N then count:= count+1; A[v]:= n fi;
  S:= S union {v};
od:
seq(A[i],i=1..N); # Robert Israel, Feb 09 2020

Extensions

Name changed by Robert Israel, Feb 09 2020

A050130 a(n)=least k satisfying a(k)=2*k in A050128.

Original entry on oeis.org

2, 4, 5, 7, 10, 11, 13, 16, 18, 21, 23, 25, 28, 30, 33, 35, 38, 41, 43, 45, 47, 49, 52, 54, 57, 59, 62, 65, 67, 69, 72, 74, 77, 79, 82, 83, 85, 87, 89, 92, 94, 95, 97, 100, 102, 105, 107, 110, 113, 115, 117, 120, 122, 125, 127, 130, 131
Offset: 1

Views

Author

Clark Kimberling

Keywords

A050131 Numbers k such that A050128(k) < A050128(k+1).

Original entry on oeis.org

1, 3, 4, 6, 9, 10, 12, 15, 17, 20, 22, 24, 27, 29, 32, 34, 37, 40, 42, 44, 46, 48, 51, 53, 56, 58, 61, 64, 66, 68, 71, 73, 76, 78, 81, 82, 84, 86, 88, 91, 93, 94, 96, 99, 101, 104, 106, 109, 112, 114, 116, 119, 121, 124, 126, 129, 130
Offset: 1

Views

Author

Clark Kimberling

Keywords

A050136 a(n) = floor(a(n-1)/2) if this is not among 0,a(1),...,a(n-1), otherwise a(n)=5*n.

Original entry on oeis.org

1, 10, 5, 2, 25, 12, 6, 3, 45, 22, 11, 60, 30, 15, 7, 80, 40, 20, 95, 47, 23, 110, 55, 27, 13, 130, 65, 32, 16, 8, 4, 160, 165, 82, 41, 180, 90, 190, 195, 97, 48, 24, 215, 107, 53, 26, 235, 117, 58, 29, 14, 260, 265, 132, 66, 33, 285, 142, 71, 35, 17, 310, 155, 77, 38, 19, 9, 340, 170, 85, 42, 21
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

Does this sequence contain every positive integer exactly once?

Links

Crossrefs

Cf. A050000, A050128, A050132, A050135.

Programs

  • Maple
    S:= {0,1}: A[1]:= 1:
for n from 2 to 100 do
  v:= floor(A[n-1]/2);
  if not member(v,S) then A[n]:= v
  else A[n]:= 5*n
  fi;
  S:= S union {A[n]};
od:
seq(A[i],i=1..100); # Robert Israel, Aug 07 2018
  • Mathematica
    f[s_List] := Block[{len = Length@s, m = Floor[s[[-1]]/2]}, Append[s, If[MemberQ[s, m], 5 len, m]]]; Rest@ Nest[f, {0, 1}, 65] (* Robert G. Wilson v, Aug 07 2018 *)

Extensions

Corrected by Robert Israel, Aug 07 2018

A050416 a(1)=a(2)=1, then a(n+1) = floor(a(n)/3) if this is not among 0, a(1), ..., a(n); otherwise a(n+1) = a(n) + a(n-1).

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 13, 4, 17, 21, 7, 28, 9, 37, 12, 49, 16, 65, 81, 27, 108, 36, 144, 48, 192, 64, 256, 85, 341, 113, 454, 151, 50, 201, 67, 22, 89, 29, 118, 39, 157, 52, 209, 69, 23, 92, 30, 10, 40, 50, 90, 140, 46, 15, 61, 20, 6, 26, 32
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

Numbers appearing among the terms more than once include 1, 50, 265, 341, 516, 570, 622, ... - Ivan Neretin, Sep 04 2015

Links

Crossrefs

Cf. A050417.
Cf. A050000, A050004, A050076, A050080, A050084, A050104, A050124, A050128, A050132, A050135, A050136, A050137, A050138, A050139, A050170, A050196.

Programs

  • Mathematica
    a = {0, 1, 1}; Do[AppendTo[a, If[MemberQ[a, c = Quotient[a[[-1]], 3]], a[[-1]] + a[[-2]], c]], {n, 3, 59}]; Delete[a, 1] (* Ivan Neretin, Sep 04 2015 *)

A050138 a(1)=2, a(2)=6. For n >= 2, a(n) = floor(a(n-1)/2) if this is not among 0,a(1),...,a(n-1); otherwise a(n) = 3*n.

Original entry on oeis.org

2, 6, 3, 1, 15, 7, 21, 10, 5, 30, 33, 16, 8, 4, 45, 22, 11, 54, 27, 13, 63, 31, 69, 34, 17, 78, 39, 19, 9, 90, 93, 46, 23, 102, 51, 25, 12, 114, 57, 28, 14, 126, 129, 64, 32, 138, 141, 70, 35, 150, 75, 37, 18, 162, 81, 40, 20, 174, 87, 43
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

Does this sequence contain every positive integer exactly once?
Inverse: 4, 1, 3, 14, 9, 2, 6, 13, 29, 8, 17, 37, 20, 41, 5, 12, 25, 53, ..., . - Robert G. Wilson v, Apr 09 2018

Links

Crossrefs

Cf. A050000, A050128, A050135, A050136, A050136, A050138.

Programs

  • Maple
    S:= {0,2,6}: A[1]:= 2: A[2]:= 6:
for n from 3 to 100 do
  t:= floor(A[n-1]/2);
  if member(t, S) then t:= 3*n fi;
  A[n]:= t;
  S:= S union {t};
od:
seq(A[n],n=1..100); # Robert Israel, Apr 09 2018
  • Mathematica
    f[s_] := Block[{b = Floor[s[[-1]]/2], l = Length@ s}, Append[s, If[MemberQ[s, b], 3l, b]]]; s = {0, 2, 6}; Nest[f, s, 57] (* Robert G. Wilson v, Apr 09 2018 *)

Extensions

Name corrected by Robert Israel, Apr 09 2018

A050137 a(1)=2; a(n) = floor(a(n-1)/2) if this is not among 0,a(1),...,a(n-1); otherwise a(n) = 2*n.

Original entry on oeis.org

2, 1, 6, 3, 10, 5, 14, 7, 18, 9, 4, 24, 12, 28, 30, 15, 34, 17, 8, 40, 20, 44, 22, 11, 50, 25, 54, 27, 13, 60, 62, 31, 66, 33, 16, 72, 36, 76, 38, 19, 82, 41, 86, 43, 21, 92, 46, 23, 98, 49, 102, 51, 106, 53, 26, 112, 56, 116, 58, 29, 122, 61
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

Does this sequence contain every positive integer exactly once?

Links

Crossrefs

Cf. A050000, A050004, A050128, A050132, A050135, A050136, A050138, A050196.

Programs

  • Maple
    R:= 2: S:= {2}: a:= 2:
for n from 2 to 100 do
  t:= floor(a/2);
  if t <> 0 and not member(t,S) then a:= t else a:= 2*n fi;
  R:= R,a; S:= S union {a};
od:
R; # Robert Israel, Aug 03 2025

A050139 a(1)=2; for n > 1, a(n) = floor(a(n-1)/2) if this is not among 0, a(1), ..., a(n-1); otherwise a(n) = 4*n.

Original entry on oeis.org

2, 1, 12, 6, 3, 24, 28, 14, 7, 40, 20, 10, 5, 56, 60, 30, 15, 72, 36, 18, 9, 4, 92, 46, 23, 11, 108, 54, 27, 13, 124, 62, 31, 136, 68, 34, 17, 8, 156, 78, 39, 19, 172, 86, 43, 21, 188, 94, 47, 200, 100, 50, 25, 216, 220, 110, 55, 232, 116
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

Does this sequence contain every positive integer exactly once?

Links

Crossrefs

Cf. A050000, A050128, A050132, A050135, A050136.

Programs

  • Mathematica
    Delete[#, 3] &@ Nest[Append[#1, If[FreeQ[#1, #2], #2, 4 #3]] & @@ {#, Floor[#[[-1]]/2], Length@ #} &, {2}, 59] (* Michael De Vlieger, Oct 06 2019 *)
Showing 1-8 of 8 results.

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