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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.
0
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.
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
KEYWORD
nonn,base
AUTHOR
Jeffrey Shallit, Jan 25 2018
STATUS
approved