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

Author

Clark Kimberling, Aug 04 2022

Keywords

• nonn
• easy

Examples

			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,...).
		

Links

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

Crossrefs

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

Programs

Mathematica

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

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

Formula

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