A383425 Indices k such that A003849(k) = 0 and A383422(k) = 1.

2, 5, 8, 13, 16, 20, 23, 24, 26, 31, 34, 37, 41, 42, 45, 49, 52, 55, 60, 63, 66, 70, 71, 73, 78, 81, 84, 89, 92, 96, 99, 100, 102, 107, 110, 113, 117, 118, 121, 125, 128, 131, 136, 139, 143, 146, 147, 149, 154, 157, 160, 164, 165, 168, 172, 175, 176, 178

Offset: 1

Author

Clark Kimberling, Apr 27 2025

Keywords

• nonn

Comments

The positive integers are partitioned by this sequence together with A383423, A383424, and A383426.

Conjecture: {a(n) - a(n-1), n>=2} = {1, 2, 3, 4, 5}.

Crossrefs

Cf. A003849, A383422, A383423, A383424, 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[[#]] == 0 && wL[[#]] == 1 &]