A316325 -id:A316325 - cp's OEIS frontend

A305389 A ternary tribonacci sequence: define the morphism f: 1 -> 2, 2 -> 3, 3 -> 1,2,3; let S[k] be result of applying f k times to 1, for k =- 0,1,2,...; sequence gives limit S[3k] as k -> oo.

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

Offset: 0

N. J. A. Sloane, Jun 21 2018

nonn

N. J. A. Sloane, Table of n, a(n) for n = 0..25280

The three sequence A305389, A305390, A305391 together give the limiting forms of the rows of A059832.

See A316324, A316325, A316326 for indices of 1's, 2's, 3's respectively.

A316324 Indices of 1's in A305389.

Original entry on oeis.org

0, 5, 9, 14, 19, 23, 28, 31, 36, 40, 45, 49, 54, 57, 62, 66, 71, 76, 80, 85, 88, 93, 97, 102, 107, 111, 116, 119, 124, 128, 133, 137, 142, 145, 150, 154, 159, 164, 168, 173, 176, 181, 185, 190, 193, 198, 202, 207, 212, 216, 221, 224, 229, 233, 238, 242, 247, 250, 255, 259, 264, 269, 273, 278

Offset: 1

N. J. A. Sloane, Jul 09 2018

nonn

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

Cf. A305389.

A316324, A316325, A316326 have the same relation to A305389 as A003144, A003145, A003146 do to the ternary tribonacci word A080843 (or A092782).

f:= 'f':
f(1):= 2: f(2):= 3: f(3):= (1,2,3):
S:= [1];
for i from 1 to 5 do T:= map(f,S); U:= map(f,T); S:= map(f,U); od:
select(t -> S[t+1]=1, [$0..nops(S)-1]); # Robert Israel, May 07 2019

A316326 Indices of 3's in A305389.

Original entry on oeis.org

2, 4, 7, 8, 11, 13, 16, 18, 21, 22, 25, 27, 30, 33, 35, 38, 39, 42, 44, 47, 48, 51, 53, 56, 59, 61, 64, 65, 68, 70, 73, 75, 78, 79, 82, 84, 87, 90, 92, 95, 96, 99, 101, 104, 106, 109, 110, 113, 115, 118, 121, 123, 126, 127, 130, 132, 135, 136, 139, 141, 144, 147, 149, 152, 153, 156, 158, 161, 163, 166, 167, 170, 172

Offset: 1

N. J. A. Sloane, Jul 09 2018

nonn

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

Cf. A305389.

A316324, A316325, A316326 have the same relation to A305389 as A003144, A003145, A003146 do to the ternary tribonacci word A080843 (or A092782).

f:= 'f':
f(1):= 2: f(2):= 3: f(3):= (1,2,3):
S:= [1];
for i from 1 to 5 do T:= map(f,S); U:= map(f,T); S:= map(f,U); od:
select(t -> S[t+1]=3, [$0..nops(S)-1]); # Robert Israel, May 07 2019

A107795 First differences of indices of 2's in A305389.

Original entry on oeis.org

2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 3, 2, 3, 4, 2, 3, 4, 2, 3, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 3, 2, 3, 4, 2, 3, 4, 2, 3, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 3, 2, 3, 4, 2, 3, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 3, 2, 3, 4, 2, 3, 4, 2, 3, 3, 2, 3, 4, 2, 3, 2, 3, 4, 2, 3, 3, 2, 3, 4, 2, 3, 4

Offset: 0

Roger L. Bagula, Jun 11 2005

nonn

Average gap=N[Apply[Plus, b]/Length[b]]=2.83843

First differences of A316325.

Edited by N. J. A. Sloane, Jul 09 2018

cp's OEIS Frontend

A305389 A ternary tribonacci sequence: define the morphism f: 1 -> 2, 2 -> 3, 3 -> 1,2,3; let S[k] be result of applying f k times to 1, for k =- 0,1,2,...; sequence gives limit S[3k] as k -> oo.

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A316324 Indices of 1's in A305389.

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A316326 Indices of 3's in A305389.

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A107795 First differences of indices of 2's in A305389.

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