A183212 -id:A183212 - cp's OEIS frontend

A178931 This sequence S is generated by the following rules: 2 is in S, and if n is in S, then floor[(3n-1)/2] and 3n are in S.

2, 6, 8, 11, 16, 18, 23, 24, 26, 33, 34, 35, 38, 48, 49, 50, 52, 54, 56, 69, 71, 72, 73, 74, 77, 78, 80, 83, 99, 102, 103, 105, 106, 107, 109, 110, 114, 115, 116, 119, 124, 144, 147, 148, 150, 152, 154, 156, 157, 158, 160, 162, 163, 164, 168, 170, 172, 173, 178, 185

Offset: 1

Clark Kimberling, Dec 30 2010

nonn

This sequence results from flattening and sorting the tree at A183212. Complement of A183213, obtained from the tree at A183211.

Sequence A117943 is the characteristic sequence of this one. - M. F. Hasler, Mar 07 2015

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

Cf. A183213, A183212.

nn=200; t={2}; t0=t; While[t=Select[Union[t,Floor[(3*t-1)/2],3*t], #<=nn &]; t0 != t, t0=t]; t

(See the Mathematica code.)

A183211 First of two trees generated by floor[(3n-1)/2].

Original entry on oeis.org

1, 3, 4, 9, 5, 12, 13, 27, 7, 15, 17, 36, 19, 39, 40, 81, 10, 21, 22, 45, 25, 51, 53, 108, 28, 57, 58, 117, 59, 120, 121, 243, 14, 30, 31, 63, 32, 66, 67, 135, 37, 75, 76, 153, 79, 159, 161, 324, 41, 84, 85, 171, 86, 174, 175, 351, 88, 177

Offset: 1

Clark Kimberling, Dec 30 2010

nonn

This tree grows from (L(1),U(1))=(1,3). The second tree, A183212, grows from (L(2),U(2))=(2,6). Here, L(n)=floor[(3n-1)/2] and U(n)=3n. The two trees are complementary in the sense that every positive integer is in exactly one tree. The sequence formed by taking the terms of this tree in increasing order is A183213. Leftmost branch of this tree: A183207. Rightmost: A000244. See A183170 and A183171 for the two trees generated by the Beatty sequence of sqrt(2).

			First four levels of the tree:
.......................1
.......................3
..............4..................9
............5...12............13....27

Ivan Neretin, Table of n, a(n) for n = 1..8192

Cf. A183170, A183212, A001651, A008585, A183209, A183213.

a = {1, 3}; row = {a[[-1]]}; Do[a = Join[a, row = Flatten[{Quotient[3 # - 1, 2], 3 #} & /@ row]], {n, 5}]; a (* Ivan Neretin, May 25 2015 *)

See the formula at A183209, but use L(n)=floor[(3n-1)/2] and U(n)=3n instead of L(n)=floor(3n/2) and U(n)=3n-1.

A183213 Ordering of the numbers in the set S generated by these rules: 1 is in S, and if n is in S, then floor[(3n-1)/2] and 3n are in S.

Original entry on oeis.org

1, 3, 4, 5, 7, 9, 10, 12, 13, 14, 15, 17, 19, 20, 21, 22, 25, 27, 28, 29, 30, 31, 32, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 51, 53, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 75, 76, 79, 81, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 101, 104, 108, 111, 112, 113, 117, 118, 120, 121, 122, 123, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135

Offset: 1

Clark Kimberling, Dec 30 2010

nonn

This sequence results from flattening and sorting the tree at A183211. Complement of A178931, obtained from the tree at A183212.

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

Cf. A183211, A178931.

nn=200; t={1}; t0=t; While[t=Select[Union[t,Floor[(3*t-1)/2],3*t], #<=nn &]; t0 != t, t0=t]; t
f[s_List] := Select[ Union@ Join[s, Floor[(3 s - 1)/2], 3 s], # < 201 &]; NestWhile[f, {1}, UnsameQ, All]

(See the Mathematica code.)

cp's OEIS Frontend

A178931 This sequence S is generated by the following rules: 2 is in S, and if n is in S, then floor[(3n-1)/2] and 3n are in S.

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A183211 First of two trees generated by floor[(3n-1)/2].

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A183213 Ordering of the numbers in the set S generated by these rules: 1 is in S, and if n is in S, then floor[(3n-1)/2] and 3n are in S.

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