A050000 -id:A050000 - cp's OEIS frontend

A050001 a(n)=position of n in A050000.

1, 5, 2, 4, 19, 6, 16, 26, 3, 18, 23, 28, 10, 15, 20, 25, 61, 7, 12, 35, 17, 22, 76, 27, 45, 130, 9, 14, 135, 37, 73, 91, 24, 60, 127, 29, 47, 65, 11, 34, 52, 70, 88, 478, 21, 75, 124, 93, 359, 44, 62, 129, 594, 8, 49, 116, 13, 134, 506, 36, 54, 431, 72, 90, 139, 480, 41, 59

Offset: 1

Clark Kimberling

Inverse permutation to A050000: a(A050000(n)) = A050000(a(n)) = n.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

a(n) = k <=> A050000(k) = n.

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a050001 n = (fromJust $ elemIndex n a050000_list) + 1
-- Reinhard Zumkeller, Nov 13 2011

More terms from Ray Chandler, Nov 16 2003

A050002 Numbers k such that A050000(k) < A050000(k+1).

Original entry on oeis.org

1, 2, 5, 6, 7, 10, 12, 16, 19, 20, 23, 26, 28, 29, 30, 35, 37, 38, 41, 45, 47, 49, 52, 54, 56, 61, 62, 65, 66, 70, 73, 76, 77, 79, 82, 84, 88, 91, 93, 95, 96, 97, 102, 104, 106, 110, 112, 116, 118, 119, 124, 127, 130, 131, 135, 136, 139

Offset: 1

Clark Kimberling

A050003 Numbers k such that A050000(k) > A050000(k+1).

Original entry on oeis.org

3, 4, 8, 9, 11, 13, 14, 15, 17, 18, 21, 22, 24, 25, 27, 31, 32, 33, 34, 36, 39, 40, 42, 43, 44, 46, 48, 50, 51, 53, 55, 57, 58, 59, 60, 63, 64, 67, 68, 69, 71, 72, 74, 75, 78, 80, 81, 83, 85, 86, 87, 89, 90, 92, 94, 98, 99, 100, 101, 103

Offset: 1

Clark Kimberling

A050128 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

1, 4, 2, 8, 10, 5, 14, 7, 3, 20, 22, 11, 26, 13, 6, 32, 16, 36, 18, 9, 42, 21, 46, 23, 50, 25, 12, 56, 28, 60, 30, 15, 66, 33, 70, 35, 17, 76, 38, 19, 82, 41, 86, 43, 90, 45, 94, 47, 98, 49, 24, 104, 52, 108, 54, 27, 114, 57, 118, 59, 29, 124

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, A050129, A050130, A050131, A050132.

N:= 100: # for a(1)..a(N)
V:= Vector(N): S:= {0,1}:
V[1]:= 1:
for n from 2 to N do
  v:= floor(V[n-1]/2);
  if member(v, S) then V[n]:= 2*n
  else V[n]:= v
  fi;
  S:= S union {V[n]}
od:
convert(V,list); # Robert Israel, Feb 09 2020

f[s_List] := Block[{len = Length@s, m = Floor[s[[-1]]/2]}, Append[s, If[MemberQ[s, m], 2 len, m]]]; Rest@Nest[f, {0, 1}, 65] (* Robert G. Wilson v, Aug 09 2018 *)

A050004 a(n) = floor(a(n-1)/2) if this is not among 0, a(1), ..., a(n-2); otherwise a(n) = 5*a(n-1).

Original entry on oeis.org

1, 5, 2, 10, 50, 25, 12, 6, 3, 15, 7, 35, 17, 8, 4, 20, 100, 500, 250, 125, 62, 31, 155, 77, 38, 19, 9, 45, 22, 11, 55, 27, 13, 65, 32, 16, 80, 40, 200, 1000, 5000, 2500, 1250, 625, 312, 156, 78, 39, 195, 97, 48, 24, 120, 60, 30, 150

Offset: 1

Clark Kimberling

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

Cf. A050000 and references therein.

Rest@Nest[Append[#, If[FreeQ[#, r = Quotient[#[[-1]], 2]], r, 5 #[[-1]]]] &, {0, 1}, 55] (* Ivan Neretin, Jul 31 2016 *)

A050132 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

1, 6, 3, 12, 15, 7, 21, 10, 5, 2, 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, 111, 55, 117, 58, 29, 14, 129, 64, 32, 138, 141, 70, 35, 150, 75, 37, 18, 162, 81, 40, 20, 174, 87, 43

Offset: 1

Clark Kimberling

nonn

This sequence is a permutation of the natural numbers. Sketch of proof: that it is one-to-one is trivial. Inductively, the halving operation can never happen more than 4 times in a row. There are at least 5 multiples of 3 amongst 16m .. 16m+15; by the induction, one of these will be a value a(n) = 3n and then 4 halving operations will get m (if it has not previously appeared). It follows that m will occur in the sequence no later than floor((16m+26)/3). Empirically, it appears that the 26 in this formula could be replaced by 21. The first occurrence of 4 consecutive halvings starts at n = 226, winding up with a(230)=42. - Franklin T. Adams-Watters, Mar 10 2006

Cf. A050000.

A050196 a(1) = 1, a(n) = floor(a(n-1)/2) if this is not among 0,a(1),...,a(n-1); otherwise a(n) = a(n-1) + a(n-2).

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 4, 12, 6, 18, 9, 27, 13, 40, 20, 10, 30, 15, 7, 22, 11, 33, 16, 49, 24, 73, 36, 109, 54, 163, 81, 244, 122, 61, 183, 91, 45, 136, 68, 34, 17, 51, 25, 76, 38, 19, 57, 28, 14, 42, 21, 63, 31, 94, 47, 23, 70, 35, 105, 52, 26

Offset: 1

Clark Kimberling

nonn

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

Cf. A050000.

Nest[Append[#, If[MemberQ[Append[#, 0], r = Quotient[#[[-1]], 2]], #[[-1]] + #[[-2]], r]] &, {1, 1}, 59] (* Ivan Neretin, Mar 02 2016 *)

A050012 a(n) = floor(a(n-1)/2) if this is positive and not yet in the sequence, otherwise a(n) = 7*a(n-1).

Original entry on oeis.org

1, 7, 3, 21, 10, 5, 2, 14, 98, 49, 24, 12, 6, 42, 294, 147, 73, 36, 18, 9, 4, 28, 196, 1372, 686, 343, 171, 85, 595, 297, 148, 74, 37, 259, 129, 64, 32, 16, 8, 56, 392, 2744, 19208, 9604, 4802, 2401, 1200, 600, 300, 150, 75, 525, 262

Offset: 1

Clark Kimberling

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

Cf. A050000 and references therein.

Rest@Nest[Append[#, If[FreeQ[#, r = Quotient[#[[-1]], 2]], r, 7 #[[-1]]]] &, {0, 1}, 52] (* Ivan Neretin, Jul 31 2016 *)

first(n)=my(v=vector(n),t); v[1]=1; for(i=2,n, t=v[i-1]\2; if(t<2, v[i]=7*v[i-1]; next); for(j=1,i-1, if(v[j]==t, v[i]=7*v[i-1]; next(2))); v[i]=t); v \\ Charles R Greathouse IV, Jul 31 2016

A050076 a(n) = floor(a(n-1)/3) if this is not among 0, a(1), ..., a(n-2); otherwise a(n) = 2*a(n-1).

Original entry on oeis.org

1, 2, 4, 8, 16, 5, 10, 3, 6, 12, 24, 48, 96, 32, 64, 21, 7, 14, 28, 9, 18, 36, 72, 144, 288, 576, 192, 384, 128, 42, 84, 168, 56, 112, 37, 74, 148, 49, 98, 196, 65, 130, 43, 86, 172, 57, 19, 38, 76, 25, 50, 100, 33, 11, 22, 44, 88, 29, 58

Offset: 1

Clark Kimberling

nonn

This permutation of the natural numbers is the "MD sequence" for (M,D) = (2,3). See A050000. - Clark Kimberling, Jun 30 2004

T. D. Noe, Table of n, a(n) for n = 1..10000
Clark Kimberling, Unsolved Problems and Rewards.

Cf. A050000 and references therein.

Rest@Nest[Append[#, If[FreeQ[#, r = Quotient[#[[-1]], 3]], r, 2 #[[-1]]]] &, {0, 1}, 60] (* Ivan Neretin, Jul 31 2016 *)

A050080 a(n) = floor(a(n-1)/3) if this is not among 0, a(1), ..., a(n-2); otherwise a(n) = 4*a(n-1).

Original entry on oeis.org

1, 4, 16, 5, 20, 6, 2, 8, 32, 10, 3, 12, 48, 192, 64, 21, 7, 28, 9, 36, 144, 576, 2304, 768, 256, 85, 340, 113, 37, 148, 49, 196, 65, 260, 86, 344, 114, 38, 152, 50, 200, 66, 22, 88, 29, 116, 464, 154, 51, 17, 68, 272, 90, 30, 120, 40, 13

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]], 3]], r, 4 #[[-1]]]] &, {0, 1}, 56] (* Ivan Neretin, Jul 31 2016 *)

cp's OEIS Frontend

A050001 a(n)=position of n in A050000.

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A050002 Numbers k such that A050000(k) < A050000(k+1).

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A050003 Numbers k such that A050000(k) > A050000(k+1).

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A050128 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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A050004 a(n) = floor(a(n-1)/2) if this is not among 0, a(1), ..., a(n-2); otherwise a(n) = 5*a(n-1).

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A050132 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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A050196 a(1) = 1, a(n) = floor(a(n-1)/2) if this is not among 0,a(1),...,a(n-1); otherwise a(n) = a(n-1) + a(n-2).

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Mathematica

A050012 a(n) = floor(a(n-1)/2) if this is positive and not yet in the sequence, otherwise a(n) = 7*a(n-1).

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PARI

A050076 a(n) = floor(a(n-1)/3) if this is not among 0, a(1), ..., a(n-2); otherwise a(n) = 2*a(n-1).

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Mathematica

A050080 a(n) = floor(a(n-1)/3) if this is not among 0, a(1), ..., a(n-2); otherwise a(n) = 4*a(n-1).

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