A363121 Primitive terms of A116882: terms k of A116882 such that k/2 is not a term of A116882.

1, 12, 40, 56, 144, 176, 208, 240, 544, 608, 672, 736, 800, 864, 928, 992, 2112, 2240, 2368, 2496, 2624, 2752, 2880, 3008, 3136, 3264, 3392, 3520, 3648, 3776, 3904, 4032, 8320, 8576, 8832, 9088, 9344, 9600, 9856, 10112, 10368, 10624, 10880, 11136, 11392, 11648, 11904

Offset: 1

Author

Amiram Eldar, May 16 2023

Keywords

• nonn
• easy

Comments

If k is a term of this sequence then k*2^m is a term of A116882 for any m >= 0.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A070941, A116882.

Programs

Mathematica

q[n_] := 2^(2*IntegerExponent[n, 2]) >= n; Join[{1}, Select[Range[2, 12000, 2], q[#] && !q[#/2] &]]
(* or *)
a[1] = 1; a[n_] := (2*n - 1)*2^IntegerLength[2*n - 1, 2]; Array[a, 100]

PARI

a(n) = if(n == 1, 1, (2*n - 1)*2^length(binary(2*n - 1)));

Python

def A363121(n): return (m:=2*n-1)<1 else 1 # Chai Wah Wu, May 17 2023

Formula

a(n) = (2*n-1)*2^A070941(n-1), for n > 1.