A287579 -id:A287579 - cp's OEIS frontend

A287576 Start with 0 and repeatedly substitute 0->0321, 1->3210, 2->2103, 3->1032.

0, 3, 2, 1, 1, 0, 3, 2, 2, 1, 0, 3, 3, 2, 1, 0, 3, 2, 1, 0, 0, 3, 2, 1, 1, 0, 3, 2, 2, 1, 0, 3, 2, 1, 0, 3, 3, 2, 1, 0, 0, 3, 2, 1, 1, 0, 3, 2, 1, 0, 3, 2, 2, 1, 0, 3, 3, 2, 1, 0, 0, 3, 2, 1, 1, 0, 3, 2, 2, 1, 0, 3, 3, 2, 1, 0, 0, 3, 2, 1, 0, 3, 2, 1, 1, 0

Offset: 1

Clark Kimberling, Jun 01 2017

This is the fixed point of the morphism 0->0231, 1->2310, 2->3102, 3->1023 starting with 0. Let t be the (nonperiodic) sequence of positions of 0, and likewise, u for 1, v for 2, and w for 3; then t(n)/n -> 4, u(n)/n -> 4, v(n)/n -> 4, w(n)/n -> 4. Also, t(n) + u(n) + v(n) + w(n) = 16*n - 6 for n >= 1. See A287556 for a guide to related sequences.

			First three iterations of the morphism:
0321
0321103221033210
0321103221033210321003211032210321033210032110321032210332100321

Clark Kimberling, Table of n, a(n) for n = 1..20000
Index entries for sequences that are fixed points of mappings

Cf. A287577, A287578, A287579, A287580.

s = Nest[Flatten[# /. {0 -> {0,3,2,1}, 1 -> {3,2,1,0}, 2 -> {2,1,0,3}, 3 -> {1,0,3,2}}] &, {0}, 9];   (* A287576 *)
Flatten[Position[s, 0]]; (* A287577 *)
Flatten[Position[s, 1]]; (* A287578 *)
Flatten[Position[s, 2]]; (* A287579 *)
Flatten[Position[s, 3]]; (* A287580 *)

a(n) = 4n - A287578(n) for n >= 1.

A287577 Positions of 0 in A287576.

Original entry on oeis.org

1, 6, 11, 16, 20, 21, 26, 31, 35, 40, 41, 46, 50, 55, 60, 61, 66, 71, 76, 77, 81, 86, 91, 96, 100, 101, 106, 111, 115, 120, 121, 126, 131, 136, 137, 142, 146, 151, 156, 157, 161, 166, 171, 176, 180, 181, 186, 191, 196, 197, 202, 207, 211, 216, 217, 222, 226

Offset: 1

Clark Kimberling, Jun 01 2017

a(n) - a(n-1) is in {1,4,5} for n >= 1; also, 4n - a(n) is in {0,1,2,3} for n >= 1.  The first 20 numbers 4n - a(n) are 3, 2, 1, 0, 0, 3, 2, 1, 1, 0, 3, 2, 2, 1, 0, 3, 2, 1, 0, 3, with
in positions given by A287578,
in positions given by A287579,
in positions given by A287580,
in positions given by A287577.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A287576, A287578, A287579, A287580.

s = Nest[Flatten[# /. {0 -> {0,3,2,1}, 1 -> {3,2,1,0}, 2 -> {2,1,0,3}, 3 -> {1,0,3,2}}] &, {0}, 9];   (* A287576 *)
Flatten[Position[s, 0]]; (* A287577 *)
Flatten[Position[s, 1]]; (* A287578 *)
Flatten[Position[s, 2]]; (* A287579 *)
Flatten[Position[s, 3]]; (* A287580 *)

A287580 Positions of 3 in A287576.

Original entry on oeis.org

2, 7, 12, 13, 17, 22, 27, 32, 36, 37, 42, 47, 51, 56, 57, 62, 67, 72, 73, 78, 82, 87, 92, 93, 97, 102, 107, 112, 116, 117, 122, 127, 132, 133, 138, 143, 147, 152, 153, 158, 162, 167, 172, 173, 177, 182, 187, 192, 193, 198, 203, 208, 212, 213, 218, 223, 227

Offset: 1

Clark Kimberling, Jun 01 2017

a(n) - a(n-1) is in {1,4,5} for n >= 1; also, 4n - a(n) is in {0,1,2,3} for n >= 1.  The first 20 numbers 4n - a(n) are 2, 1, 0, 3, 3, 2, 1, 0, 0, 3, 2, 1, 1, 0, 3, 2, 1, 0, 3, 2, with
in positions given by A287579,
in positions given by A287580,
in positions given by A287577,
in positions given by A287578.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A287576, A287577, A287578, A287579.

s = Nest[Flatten[# /. {0 -> {0,3,2,1}, 1 -> {3,2,1,0}, 2 -> {2,1,0,3}, 3 -> {1,0,3,2}}] &, {0}, 9];   (* A287576 *)
Flatten[Position[s, 0]]; (* A287577 *)
Flatten[Position[s, 1]]; (* A287578 *)
Flatten[Position[s, 2]]; (* A287579 *)
Flatten[Position[s, 3]]; (* A287580 *)

a(n) = 4n - A287576(n) for n >= 1.

A287578 Positions of 1 in A287576.

Original entry on oeis.org

4, 5, 10, 15, 19, 24, 25, 30, 34, 39, 44, 45, 49, 54, 59, 64, 65, 70, 75, 80, 84, 85, 90, 95, 99, 104, 105, 110, 114, 119, 124, 125, 130, 135, 140, 141, 145, 150, 155, 160, 164, 165, 170, 175, 179, 184, 185, 190, 195, 200, 201, 206, 210, 215, 220, 221, 225

Offset: 1

Clark Kimberling, Jun 01 2017

a(n) - a(n-1) is in {1,4,5} for n >= 1; also, 4n - a(n) is in {0,1,2,3} for n >= 1.  The first 20 numbers 4n - a(n) are 0, 3, 2, 1, 1, 0, 3, 2, 2, 1, 0, 3, 3, 2, 1, 0, 3, 2, 1, 0, with
in positions given by A287577,
in positions given by A287578,
in positions given by A287579,
in positions given by A287580.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A287576, A287577, A287579, A287580.

s = Nest[Flatten[# /. {0 -> {0,3,2,1}, 1 -> {3,2,1,0}, 2 -> {2,1,0,3}, 3 -> {1,0,3,2}}] &, {0}, 9];   (* A287576 *)
Flatten[Position[s, 0]]; (* A287577 *)
Flatten[Position[s, 1]]; (* A287578 *)
Flatten[Position[s, 2]]; (* A287579 *)
Flatten[Position[s, 3]]; (* A287580 *)

a(n) = 4n - A287576(n) for n >= 1.

cp's OEIS Frontend

A287576 Start with 0 and repeatedly substitute 0->0321, 1->3210, 2->2103, 3->1032.

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A287577 Positions of 0 in A287576.

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A287580 Positions of 3 in A287576.

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A287578 Positions of 1 in A287576.

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