A110604 Numbers n whose base 6 representations, interpreted as base 10 integers, are semiprimes.

4, 6, 10, 11, 13, 14, 17, 21, 22, 23, 31, 35, 43, 47, 49, 50, 51, 57, 58, 61, 62, 63, 65, 71, 73, 74, 75, 77, 81, 82, 83, 85, 95, 105, 106, 109, 110, 111, 113, 118, 121, 123, 130, 131, 133, 143, 147, 151, 153, 155, 158, 173, 175, 177, 178, 181, 182, 185, 187, 190, 191

Offset: 1

Author

Jonathan Vos Post, Jul 30 2005

Keywords

• base
• easy
• nonn

Comments

A108873 is the equivalent using base 3. A110602 is the equivalent using base 4. A110603 is the equivalent using base 5. A110605 is the equivalent using base 7. A110606 is the equivalent using base 8. A110607 is the equivalent using base 9.

Examples

			a(1) = 4 because 4 (base 6) = 4 and 4 (base 10) = 2 * 2, a semiprime (A001358).
a(2) = 6 because 6 (base 6) = 10 and 10 (base 10) = 2 * 5.
a(3) = 10 because 10 (base 6) = 14 and 14 (base 10) = 2 * 7.
a(4) = 11 because 11 (base 6) = 15 and 15 (base 10) = 3 * 5.
a(5) = 13 because 13 (base 6) = 21 and 21 (base 10) = 3 * 7.
		

Crossrefs

Cf. A001358, A007092, A108873, A110602, A110603, A110605, A110606, A110607.

Programs

Mathematica

Select[Range[191], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 6]]] == 2 &] (* Ray Chandler, Aug 05 2005 *)
Select[Range[200],PrimeOmega[FromDigits[IntegerDigits[#,6]]]==2&] (* Harvey P. Dale, Oct 02 2011 *)

Extensions

Corrected and extended by Ray Chandler, Aug 05 2005