login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

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.
0

%I #8 Jan 26 2018 09:02:32

%S 2,3,5,7,10,11,13,14,15,17,18,19,21,22,23,26,27,29,30,31,34,35,37,39,

%T 41,42,43,45,46,47,50,51,53,54,55,58,59,61,62,63,66,67,69,70,71,73,74,

%U 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

%N 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.

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

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

%Y Cf. A090421, which does not allow leading zeros.

%K nonn,base

%O 1,1

%A _Jeffrey Shallit_, Jan 25 2018