A110602 Numbers n whose base 4 representations, interpreted as base 10 integers, are semiprimes.

4, 9, 10, 15, 21, 25, 26, 27, 31, 33, 34, 35, 39, 41, 49, 50, 51, 57, 59, 67, 69, 81, 85, 89, 95, 98, 99, 101, 119, 122, 127, 137, 141, 143, 145, 146, 147, 154, 155, 161, 173, 178, 185, 187, 199, 202, 205, 209, 211, 215, 221, 223, 226, 235, 239, 257, 259, 265, 266

Offset

1,1

Comments

Note that this sequence begins with 7 semiprimes (A001358) but is not a subset of the semiprimes, since a(9) = 31 and 31 (base 4) = 133, which interpreted as base 10 is 133 = 7 * 19, yet 31 (base 10) is prime rather than semiprime. A108873 is the equivalent using base 3. A110603 is the equivalent using base 5. A110604 is the equivalent using base 6. A110605 is the equivalent using base 7. A110606 is the equivalent using base 8. A110607 is the equivalent using base 9.

Links

Table of n, a(n) for n=1..59.

Example

a(1) = 4 because 4 (base 4) = 10 and 10 (base 10) = 2 * 5, a semiprime (A001358).
a(2) = 9 because 10 (base 4) = 21, which interpreted base 10 is 21 = 3 * 7.
a(3) = 10 because 10 (base 4) = 22, which interpreted base 10 is 22 = 2 * 11.
a(4) = 15 because 15 (base 4) = 33, which interpreted base 10 is 33 = 3 * 11.

Mathematica

Select[Range[266], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 4]]] == 2 &] (* Ray Chandler, Aug 05 2005 *)

Crossrefs

Cf. A001358, A007090, A108873, A110603, A110604, A110605, A110606, A110607.

Sequence in context: A163643 A139558 A219556 * A254923 A122635 A191912

Adjacent sequences: A110599 A110600 A110601 * A110603 A110604 A110605

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Jul 30 2005

Extensions

Extended by Ray Chandler, Aug 05 2005

Status

approved