A356133 Complement of A026430.

2, 4, 7, 11, 13, 17, 20, 22, 25, 29, 32, 34, 38, 40, 43, 47, 49, 53, 56, 58, 62, 64, 67, 71, 74, 76, 79, 83, 85, 89, 92, 94, 97, 101, 104, 106, 110, 112, 115, 119, 122, 124, 127, 131, 133, 137, 140, 142, 146, 148, 151, 155, 157, 161, 164, 166, 169, 173, 176

Offset

1,1

Links

Winston de Greef, Table of n, a(n) for n = 1..5000

Formula

a(n) = 3n - A001285(n-1) for n >= 1.

Example

The partial sums of the Thue-Morse sequence A001285 = (1,2,2,1,2,1,1,...) are A026430 = (0,1,3,5,6,8,9,10,...), from which the missing positive integers are (2,4,7,11,...).

Mathematica

u = Accumulate[1 + ThueMorse /@ Range[0, 2^7]]; (* A026430 *)
Complement[Range[Max[u]], u]  (* A356133 *)

Prog

(PARI) a(n) = 3*n - 1 - hammingweight(n-1)%2; \\ Kevin Ryde, Aug 04 2022
(Python)
def A356133(n): return 3*n-(2 if (n-1).bit_count()&1 else 1) # Chai Wah Wu, Mar 01 2023

Crossrefs

Cf. A001285, A007413, A026430, A036580, A091855, A036554, A091855, A354384.

Sequence in context: A107791 A181518 A262231 * A191323 A307207 A165288

Adjacent sequences: A356130 A356131 A356132 * A356134 A356135 A356136

Keyword

nonn,easy

Author

Clark Kimberling, Aug 04 2022

Status

approved