A050000 -id:A050000 - cp's OEIS frontend

A050108 a(n) = floor(a(n-1)/4) if this is positive and not yet in the sequence, otherwise a(n) = 5*a(n-1).

1, 5, 25, 6, 30, 7, 35, 8, 2, 10, 50, 12, 3, 15, 75, 18, 4, 20, 100, 500, 125, 31, 155, 38, 9, 45, 11, 55, 13, 65, 16, 80, 400, 2000, 10000, 2500, 625, 156, 39, 195, 48, 240, 60, 300, 1500, 375, 93, 23, 115, 28, 140, 700, 175, 43, 215

Offset: 1

Clark Kimberling

nonn

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A050000 and references therein.

Rest@Nest[Append[#, If[FreeQ[#, r = Quotient[#[[-1]], 4]], r, 5 #[[-1]]]] &, {0, 1}, 55] (* Ivan Neretin, Jul 31 2016 *)

first(n)=my(v=vector(n),t); v[1]=1; for(i=2,n, t=v[i-1]\4; if(t<2, v[i]=5*v[i-1]; next); for(j=1,i-1, if(v[j]==t, v[i]=5*v[i-1]; next(2))); v[i]=t); v \\ Charles R Greathouse IV, Jul 31 2016

A050112 a(n) = floor(a(n-1)/4) if this is positive and not yet in the sequence, otherwise a(n) = 6*a(n-1).

Original entry on oeis.org

1, 6, 36, 9, 2, 12, 3, 18, 4, 24, 144, 864, 216, 54, 13, 78, 19, 114, 28, 7, 42, 10, 60, 15, 90, 22, 5, 30, 180, 45, 11, 66, 16, 96, 576, 3456, 20736, 5184, 1296, 324, 81, 20, 120, 720, 4320, 1080, 270, 67, 402, 100, 25, 150, 37, 222, 55

Offset: 1

Clark Kimberling

nonn

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A050000 and references therein.

Rest@Nest[Append[#, If[FreeQ[#, r = Quotient[#[[-1]], 4]], r, 6 #[[-1]]]] &, {0, 1}, 54] (* Ivan Neretin, Jul 31 2016 *)

first(n)=my(v=vector(n),t); v[1]=1; for(i=2,n, t=v[i-1]\4; if(t<2, v[i]=6*v[i-1]; next); for(j=1,i-1, if(v[j]==t, v[i]=6*v[i-1]; next(2))); v[i]=t); v \\ Charles R Greathouse IV, Jul 31 2016

A050135 a(1) = 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

1, 8, 4, 2, 20, 10, 5, 32, 16, 40, 44, 22, 11, 56, 28, 14, 7, 3, 76, 38, 19, 9, 92, 46, 23, 104, 52, 26, 13, 6, 124, 62, 31, 15, 140, 70, 35, 17, 156, 78, 39, 168, 84, 42, 21, 184, 188, 94, 47, 200, 100, 50, 25, 12, 220, 110, 55, 27, 236

Offset: 1

Clark Kimberling

nonn

Does this sequence contain every positive integer exactly once?

Cf. A050000.

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

Clark Kimberling

Does this sequence contain every positive integer exactly once?

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A050000, A050128, A050132, A050135.

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

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 *)

Corrected by Robert Israel, Aug 07 2018

A268642 Seelmann's sequence: a(1) = 1; thereafter a(n + 1) = ceiling(a(n)/2) unless this is already in the sequence, in which case a(n + 1) = 3*a(n).

Original entry on oeis.org

1, 3, 2, 6, 18, 9, 5, 15, 8, 4, 12, 36, 108, 54, 27, 14, 7, 21, 11, 33, 17, 51, 26, 13, 39, 20, 10, 30, 90, 45, 23, 69, 35, 105, 53, 159, 80, 40, 120, 60, 180, 540, 270, 135, 68, 34, 102, 306, 153, 77, 231, 116, 58, 29, 87, 44, 22, 66, 198, 99, 50, 25, 75, 38

Offset: 1

Peter Kagey, Feb 09 2016, based on a posting by David Seelmann to the Reddit web site

It is conjectured that this is a permutation of the positive integers, along with any Seelmann sequence in which a(n+1) = M*a(n) if the divide by 2 rule cannot be applied, for any integer M>1 and not of the form M = 2^N. [Corrected by Charlie Neder, Feb 06 2019]
Reminiscent of the 3x+1 or Collatz problem, cf. A006577. - N. J. A. Sloane, Feb 09 2016
The Reddit link contains what is claimed to be a proof that this sequence is a permutation. I don't know if it has been checked. - N. J. A. Sloane, Feb 11 2016

Peter Kagey, Table of n, a(n) for n = 1..10000
David Seelmann, Proving a sequence of integers reaches every integer, Posting to Reddit Web Site, Jan 09 2016

Cf. A006577, A050000 (with floor instead of ceiling).

For records see A268529, A268530. For inverse see A268531.

a[1]=1; a[n_] := a[n] = Module[{an1, an}, an1 = a[n-1]; an = If[EvenQ[an1], an1/2, (an1+1)/2]; If[FreeQ[Array[a, n-1], an], an, 3*a[n-1]]]; Array[a, 100] (* Jean-François Alcover, Feb 27 2016 *)
Fold[Append[#1, If[FreeQ[#1, #3], #3, 3 #1[[-1]]]] & @@ {#1, #2, Ceiling[#1[[-1]]/2]} &, {1}, Range@ 63] (* Michael De Vlieger, Jan 13 2018 *)

Title corrected by Charlie Neder, Feb 06 2019

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

Clark Kimberling

nonn

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

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A050417.

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

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

Clark Kimberling

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

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

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 *)

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

Clark Kimberling

Does this sequence contain every positive integer exactly once?

Robert Israel, Table of n, a(n) for n = 1..10000

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

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

Clark Kimberling

nonn

Does this sequence contain every positive integer exactly once?

Michael De Vlieger, Table of n, a(n) for n = 1..10000

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

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

cp's OEIS Frontend

A050108 a(n) = floor(a(n-1)/4) if this is positive and not yet in the sequence, otherwise a(n) = 5*a(n-1).

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A050112 a(n) = floor(a(n-1)/4) if this is positive and not yet in the sequence, otherwise a(n) = 6*a(n-1).

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A050135 a(1) = 1, a(n) = floor(a(n-1)/2) if this is not among 0,a(1),...,a(n-1); otherwise a(n) = 4*n.

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

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A268642 Seelmann's sequence: a(1) = 1; thereafter a(n + 1) = ceiling(a(n)/2) unless this is already in the sequence, in which case a(n + 1) = 3*a(n).

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Mathematica

Extensions

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).

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Mathematica

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.

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Maple

Mathematica

Extensions

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.

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Maple

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.

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