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Integers whose ternary representation consists of concatenated runs A(1)B(1)C(1)A(2)B(2)C(2)...A(k)B(k)C(k), where A(i) is a run of 1's, B(i) a run of 0's, and C(i) a run of 2's, for i = 1..k.
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%I #9 Apr 04 2024 10:28:46

%S 11,29,35,38,83,89,107,110,116,119,245,251,269,308,323,326,332,350,

%T 353,359,362,731,737,755,794,809,920,926,929,956,971,974,980,998,1037,

%U 1052,1055,1061,1079,1082,1088,1091,2189,2195,2213,2252,2267,2378,2384,2387

%N Integers whose ternary representation consists of concatenated runs A(1)B(1)C(1)A(2)B(2)C(2)...A(k)B(k)C(k), where A(i) is a run of 1's, B(i) a run of 0's, and C(i) a run of 2's, for i = 1..k.

%C a(n) == 2 mod 3 for all n.

%t Map[#[[1]] &, Select[Map[{#, DeleteDuplicates[Partition[Map[#[[1]] &, Split[IntegerDigits[#, 3]]], UpTo[3]]] == {{1, 0, 2}}} &,

%t Range[2, 2800, 3]], #[[2]] &]] (* A371105 *)

%t m = Map[{#, IntegerString[#, 3]} &, %];

%t Map[Last, ToExpression[m]] (* this sequence *)

%t (* _Peter J. C. Moses_, Mar 06 2024 *)

%Y Cf. A007088, A371105, A371107, A371108, A371109, A371110, A371111, A371112.

%K nonn,base

%O 1,1

%A _Clark Kimberling_, Mar 22 2024