A381259 Numbers obtained by concatenating powers of 2, sorted into increasing order.

1, 2, 4, 8, 11, 12, 14, 16, 18, 21, 22, 24, 28, 32, 41, 42, 44, 48, 64, 81, 82, 84, 88, 111, 112, 114, 116, 118, 121, 122, 124, 128, 132, 141, 142, 144, 148, 161, 162, 164, 168, 181, 182, 184, 188, 211, 212, 214, 216, 218, 221, 222, 224, 228, 232, 241, 242, 244, 248, 256, 264

Offset: 1

Author

Stefano Spezia, Feb 18 2025

Keywords

• nonn
• base
• easy

Comments

Take the list {2^i: i >= 0} and concatenate its terms (allowing multiple copies) in any order; then sort the result into increasing order.

The term a(32) = 128 is a power of 2 as well as the concatenation of several powers of 2. - Rémy Sigrist, Feb 20 2025

Examples

			11 is a term because it is the concatenation of 1 = 2^0 with itself;
12 is a term because it is the concatenation of 1 = 2^0 with 2 = 2^1;
32 is a term because it is equal to 2^5;
168 is a term because it is the concatenation of 16 = 2^4 with 8 = 2^3.
0 is not a term because it is not a power of 2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..11921
• Rémy Sigrist, PARI program

Crossrefs

Supersequence of A028846.

Some subsequences: A000079, A045507, A178664.

Cf. A152242.

Programs

PARI

\\ See Links section.