A110605 Numbers n whose base 7 representations, interpreted as base 10 integers, are semiprimes.

4, 6, 7, 11, 12, 15, 16, 19, 20, 24, 25, 26, 34, 36, 40, 44, 47, 55, 57, 61, 64, 65, 66, 73, 74, 78, 79, 80, 82, 83, 89, 92, 97, 99, 100, 101, 103, 104, 108, 109, 110, 113, 118, 124, 136, 137, 142, 145, 148, 149, 150, 152, 158, 162, 164, 167, 172, 173, 176, 181, 187

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. A110604 is the equivalent using base 6. A110606 is the equivalent using base 8. A110607 is the equivalent using base 9.

Examples

			a(1) = 4 because 4 (base 7) = 4 (base 10) = 2 * 2, a semiprime (A001358).
a(2) = 6 because 6 (base 7) = 6 (base 10) = 2 * 3
a(3) = 7 because 7 (base 7) = 10 and 10 (base 10) = 2 * 5.
a(4) = 11 because 11 (base 7) = 14 and 14 (base 10) = 2 * 7.
a(5) = 12 because 12 (base 7) = 15 and 15 (base 10) = 3 * 5.
		

Crossrefs

Cf. A001358, A007093, A108873, A110602, A110603, A110604, A110606, A110607.

Programs

Mathematica

Select[Range[187], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 7]]] == 2 &] (* Ray Chandler, Aug 05 2005 *)

Extensions

Extended by Ray Chandler, Aug 05 2005