A298746 Numbers n whose base-2 representation can be written as the concatenation of the base-2 representations of a list of prime numbers, allowing leading zeros.

2, 3, 5, 7, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 26, 27, 29, 30, 31, 34, 35, 37, 39, 41, 42, 43, 45, 46, 47, 50, 51, 53, 54, 55, 58, 59, 61, 62, 63, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 98, 99, 101, 103, 106, 107, 109, 110, 111, 113, 114, 115, 117, 118

Offset: 1

Author

Jeffrey Shallit, Jan 25 2018

Keywords

• nonn
• base

Comments

Has positive density in the positive integers, which can be proved by considering only those numbers obtained using the primes 2 and 3.

Examples

			For example, 26 is such a number because 26 in base 2 is 11010, which can be written as the concatenation (11)(010).
		

Crossrefs

Cf. A090421, which does not allow leading zeros.