A383426 Indices k such that A003849(k) = 1 and A383422(k) = 0.

4, 14, 22, 25, 33, 40, 43, 51, 61, 69, 72, 80, 90, 98, 101, 108, 116, 119, 127, 137, 145, 148, 156, 163, 166, 174, 177, 184, 192, 195, 203, 213, 221, 224, 232, 239, 242, 250, 260, 268, 271, 279, 286, 289, 297

Offset: 1

Author

Clark Kimberling, Apr 27 2025

Keywords

• nonn

Comments

The positive integers are partitioned by this sequence together with A383423, A383424, and A383425.

Conjecture: {a(n) - a(n-1), n>=2} = {3, 7, 8, 10}.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003849, A383422, A383423, A383424, A383425, 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[[#]] == 1 && wL[[#]] == 0 &]

Python

from math import isqrt
from itertools import count, islice
def A383426_gen(): # generator of terms
    for n in count(1):
        if ((k:=(n+isqrt(5*n**2)&-2)-n)+1+isqrt(m:=5*(k+1)**2)>>1)-(k+isqrt(m-10*k-5)>>1)==1: yield k-1
A383426_list = list(islice(A383426_gen(),45)) # Chai Wah Wu, May 22 2025