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

1,1

Comments

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

Links

Table of n, a(n) for n=1..78.

Example

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.

Sequence in context: A125975 A046758 A121232 * A122428 A087246 A090421

Adjacent sequences: A298743 A298744 A298745 * A298747 A298748 A298749

Keyword

nonn,base

Author

Jeffrey Shallit, Jan 25 2018

Status

approved