A277735 -id:A277735 - cp's OEIS frontend

A277736 Positions of 0's in A277735.

1, 4, 5, 6, 8, 10, 13, 14, 17, 18, 21, 22, 23, 25, 28, 29, 30, 32, 35, 36, 37, 39, 41, 44, 45, 48, 49, 50, 52, 54, 57, 58, 61, 62, 63, 65, 67, 70, 71, 74, 75, 78, 79, 80, 82, 85, 86, 87, 89, 91, 94, 95, 98, 99, 102, 103, 104, 106, 109, 110, 111, 113, 115, 118, 119, 122, 123, 126, 127, 128, 130, 133, 134

Offset: 1

N. J. A. Sloane, Nov 07 2016

nonn

{A277736, A277737, A277738} forms a three-way partition of the positive integers, similar to {A003144, A003145, A003146}.

N. J. A. Sloane, Table of n, a(n) for n = 1..20000

Cf. A277735, A277737, A277738.

Cf. also A003144, A003145, A003146.

with(ListTools);
T:=proc(S) Flatten(subs( {0=[0,1], 1=[2,0], 2=[0]}, S)); end;
S:=[0];
for n from 1 to 14 do S:=T(S); od:
S; # A277735
p0:=[]: p1:=[]: p2:=[]:
for i from 1 to nops(S) do
j:=S[i];
if j=0 then p0:=[op(p0),i];
elif j=1 then p1:=[op(p1),i];
else p2:=[op(p2),i]; fi: od:
p0; # A277736
p1; # A277737
p2: # A277738

A277737 Positions of 1's in A277735.

Original entry on oeis.org

2, 7, 9, 11, 15, 19, 24, 26, 31, 33, 38, 40, 42, 46, 51, 53, 55, 59, 64, 66, 68, 72, 76, 81, 83, 88, 90, 92, 96, 100, 105, 107, 112, 114, 116, 120, 124, 129, 131, 136, 138, 143, 145, 147, 151, 156, 158, 160, 164, 168, 173, 175, 180, 182, 187, 189, 191, 195, 200, 202, 204, 208, 212, 217, 219, 224, 226

Offset: 1

N. J. A. Sloane, Nov 07 2016

nonn

{A277736, A277737, A277738} forms a three-way partition of the positive integers, similar to {A003144, A003145, A003146}.

N. J. A. Sloane, Table of n, a(n) for n = 1..19513

Cf. A277735, A277736, A277738.

Cf. also A003144, A003145, A003146.

with(ListTools);
T:=proc(S) Flatten(subs( {0=[0,1], 1=[2,0], 2=[0]}, S)); end;
S:=[0];
for n from 1 to 14 do S:=T(S); od:
S; # A277735
p0:=[]: p1:=[]: p2:=[]:
for i from 1 to nops(S) do
j:=S[i];
if j=0 then p0:=[op(p0),i];
elif j=1 then p1:=[op(p1),i];
else p2:=[op(p2),i]; fi: od:
p0; # A277736
p1; # A277737
p2: # A277738

A277738 Positions of 2's in A277735.

Original entry on oeis.org

3, 12, 16, 20, 27, 34, 43, 47, 56, 60, 69, 73, 77, 84, 93, 97, 101, 108, 117, 121, 125, 132, 139, 148, 152, 161, 165, 169, 176, 183, 192, 196, 205, 209, 213, 220, 227, 236, 240, 249, 253, 262, 266, 270, 277, 286, 290, 294, 301, 308, 317, 321, 330, 334, 343, 347, 351, 358, 367, 371, 375, 382, 389, 398

Offset: 1

N. J. A. Sloane, Nov 07 2016

nonn

{A277736, A277737, A277738} forms a three-way partition of the positive integers, similar to {A003144, A003145, A003146}.

N. J. A. Sloane, Table of n, a(n) for n = 1..10609

Cf. A277735, A277736, A277737.

Cf. also A003144, A003145, A003146.

with(ListTools);
T:=proc(S) Flatten(subs( {0=[0,1], 1=[2,0], 2=[0]}, S)); end;
S:=[0];
for n from 1 to 14 do S:=T(S); od:
S; # A277735
p0:=[]: p1:=[]: p2:=[]:
for i from 1 to nops(S) do
j:=S[i];
if j=0 then p0:=[op(p0),i];
elif j=1 then p1:=[op(p1),i];
else p2:=[op(p2),i]; fi: od:
p0; # A277736
p1; # A277737
p2: # A277738

A317953 Apply the morphism 1 -> {1, 2}, 2 -> {3,1}, 3 -> {1} n times to 1, and concatenate the resulting string.

Original entry on oeis.org

1, 12, 1231, 1231112, 1231112121231, 123111212123112311231112, 12311121212311231123111212311121231112121231, 123111212123112311231112123111212311121212311231112121231123111212123112311231112

Offset: 1

N. J. A. Sloane, Aug 21 2018

nonn

For the tribonacci word A092782, each block b(n) (see A103269) is the concatenation of the three previous blocks: b(n) = b(n-1).b(n-2).b(n-3). Instead, here we have a(n) = a(n-1).a(n-3).a(n-2), as can be seen in the examples section below.

			a(1): 1,
a(2): 12,
a(3): 1231,
a(4): 1231112,
a(5): 1231112121231,
a(6): 123111212123112311231112,
a(7): 12311121212311231123111212311121231112121231,
equals a(6).a(4).a(5), look:
a(6):123111212123112311231112,
a(4):                        1231112,
a(5):                               1231112121231,
a(8): 123111212123112311231112123111212311121212311231112121231123111212123112311231112
equals a(7).a(5).a(6), look:
a(7): 12311121212311231123111212311121231112121231,
a(5):                                             1231112121231,
a(6):                                                          123111212123112311231112,

V. F. Sirvent, Semigroups and the self-similar structure of the flipped tribonacci substitution, Applied Math. Letters, 12 (1999), 25-29.

Cf. A100619 (the limiting string), A277735, A317953.

A103269 is the analog for the word A092782.

cp's OEIS Frontend

A277736 Positions of 0's in A277735.

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A277737 Positions of 1's in A277735.

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A277738 Positions of 2's in A277735.

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A317953 Apply the morphism 1 -> {1, 2}, 2 -> {3,1}, 3 -> {1} n times to 1, and concatenate the resulting string.

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