A383424 Indices k such that A003849(k) = 1 and A383422(k) = 1.

1, 6, 9, 12, 17, 19, 27, 30, 35, 38, 46, 48, 53, 56, 59, 64, 67, 74, 77, 82, 85, 88, 93, 95, 103, 106, 111, 114, 122, 124, 129, 132, 135, 140, 142, 150, 153, 158, 161, 169, 171, 179, 182, 187, 190, 197, 200, 205, 208, 211, 216, 218, 226, 229, 234, 237, 245

Offset: 1

Author

Clark Kimberling, Apr 27 2025

Keywords

• nonn

Comments

The positive integers are partitioned by this sequence together with A383423, A383425, and A383426.

Conjecture: {a(n) - a(n-1), n>=2} = {2, 3, 5, 7, 8}.

Crossrefs

Cf. A003849, A383422, A383423, A383425, A383426, A383427.

Programs

Mathematica

wF = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 15];  (* A003849 *)
s[0] = "0"; s[1] = "011"; s[n_] := StringJoin[s[n - 1], s[n - 2]]; (* A383422 *)
wL = Join[{0}, IntegerDigits[FromDigits[s[15]]]];
-1+Select[Range[400], wF[[#]] == wL[[#]] == 1 &]