A287574 -id:A287574 - cp's OEIS frontend

A287571 Start with 0 and repeatedly substitute 0->0312, 1->3120, 2->1203, 3->2031.

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

Offset: 1

Clark Kimberling, May 31 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:
0312
0312203131201203
0312203131201203120303122031312020313120120303123120120303122031

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

Cf. A287572, A287573, A287574, A287575.

s = Nest[Flatten[# /. {0 -> {0,3,1,2}, 1 -> {3,1,2,0}, 2 -> {1,2,0,3}, 3 -> {2,0,3,1}}] &, {0}, 9];   (* A287571 *)
Flatten[Position[s, 0]]; (* A287572 *)
Flatten[Position[s, 1]]; (* A287573 *)
Flatten[Position[s, 2]]; (* A287574 *)
Flatten[Position[s, 3]]; (* A287575 *)

a(n) = 4n - A287574(n) for n >= 1.

A287572 Positions of 0 in A287571.

Original entry on oeis.org

1, 6, 12, 15, 19, 21, 26, 32, 34, 40, 43, 45, 52, 55, 57, 62, 68, 71, 73, 78, 81, 86, 92, 95, 99, 101, 106, 112, 114, 120, 123, 125, 131, 133, 138, 144, 146, 152, 155, 157, 164, 167, 169, 174, 177, 182, 188, 191, 194, 200, 203, 205, 212, 215, 217, 222, 225

Offset: 1

Clark Kimberling, May 31 2017

a(n) - a(n-1) is in {1,2,3,4,5,6,7} 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, 0, 1, 1, 3, 2, 0, 2, 0, 1, 3, 0, 1, 3, 2, 0, 1, 3, 2, with
in positions given by A287573,
in positions given by A287574,
in positions given by A287575,
in positions given by A287572.

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

Cf. A287571, A287573, A287574, A287575.

s = Nest[Flatten[# /. {0 -> {0,3,1,2}, 1 -> {3,1,2,0}, 2 -> {1,2,0,3}, 3 -> {2,0,3,1}}] &, {0}, 9];   (* A287571 *)
Flatten[Position[s, 0]]; (* A287572 *)
Flatten[Position[s, 1]]; (* A287573 *)
Flatten[Position[s, 2]]; (* A287574 *)
Flatten[Position[s, 3]]; (* A287575 *)

A287575 Positions of 3 in A287571.

Original entry on oeis.org

2, 7, 9, 16, 20, 22, 27, 29, 35, 37, 44, 46, 49, 56, 58, 63, 65, 72, 74, 79, 82, 87, 89, 96, 100, 102, 107, 109, 115, 117, 124, 126, 132, 134, 139, 141, 147, 149, 156, 158, 161, 168, 170, 175, 178, 183, 185, 192, 195, 197, 204, 206, 209, 216, 218, 223, 226

Offset: 1

Clark Kimberling, Jun 01 2017

a(n) - a(n-1) is in {1,2,3,4,5,6,7} 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, 3, 0, 0, 2, 1, 3, 1, 3, 0, 2, 3, 0, 2, 1, 3, 0, 2, 1, with
in positions given by A287574,
in positions given by A287575,
in positions given by A287572,
in positions given by A287573.

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

Cf. A287571, A287572, A287573, A287574.

s = Nest[Flatten[# /. {0 -> {0,3,1,2}, 1 -> {3,1,2,0}, 2 -> {1,2,0,3}, 3 -> {2,0,3,1}}] &, {0}, 9];   (* A287571 *)
Flatten[Position[s, 0]]; (* A287572 *)
Flatten[Position[s, 1]]; (* A287573 *)
Flatten[Position[s, 2]]; (* A287574 *)
Flatten[Position[s, 3]]; (* A287575 *)

A287573 Positions of 1 in A287571.

Original entry on oeis.org

3, 8, 10, 13, 17, 23, 28, 30, 36, 38, 41, 47, 50, 53, 59, 64, 66, 69, 75, 80, 83, 88, 90, 93, 97, 103, 108, 110, 116, 118, 121, 127, 129, 135, 140, 142, 148, 150, 153, 159, 162, 165, 171, 176, 179, 184, 186, 189, 196, 198, 201, 207, 210, 213, 219, 224, 227

Offset: 1

Clark Kimberling, Jun 01 2017

a(n) - a(n-1) is in {1,2,3,4,5,6,7} for n >= 1; also, 4n - a(n) is in {0,1,2,3} for n >= 1.  The first 20 numbers 4n - a(n) are 1, 0, 2, 3, 3, 1, 0, 2, 0, 2, 3, 1, 2, 3, 1, 0, 2, 3, 1, 0, with
in positions given by A287575,
in positions given by A287572,
in positions given by A287573,
in positions given by A287574.

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

Cf. A287571, A287572, A287574, A287575.

s = Nest[Flatten[# /. {0 -> {0,3,1,2}, 1 -> {3,1,2,0}, 2 -> {1,2,0,3}, 3 -> {2,0,3,1}}] &, {0}, 9]; (* A287571 *)
Flatten[Position[s, 0]]; (* A287572 *)
Flatten[Position[s, 1]]; (* A287573 *)
Flatten[Position[s, 2]]; (* A287574 *)
Flatten[Position[s, 3]]; (* A287575 *)

cp's OEIS Frontend

A287571 Start with 0 and repeatedly substitute 0->0312, 1->3120, 2->1203, 3->2031.

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A287572 Positions of 0 in A287571.

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A287575 Positions of 3 in A287571.

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A287573 Positions of 1 in A287571.

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