A108873 Numbers n whose base 3 representations, interpreted as base 10 integers, are semiprimes.

3, 7, 8, 13, 16, 17, 19, 20, 25, 31, 37, 40, 43, 47, 49, 61, 64, 65, 71, 73, 82, 88, 89, 92, 97, 100, 101, 106, 110, 115, 118, 121, 127, 136, 142, 143, 155, 179, 184, 187, 188, 191, 209, 232, 235, 244, 250, 254, 259, 262, 263, 265, 269, 274, 281, 289, 299, 314, 319

Offset: 1

Author

Jonathan Vos Post, Jul 13 2005

Keywords

• base
• easy
• nonn

Examples

			a(1) = 3 because 3 (base 10) = 10 (base 3) and 10 base 10 = 2 * 5.
a(2) = 7 because 7 (base 10) = 21 (base 3) and 21 base 10 = 3 * 7.
a(4) = 13 because 13 (base 10) = 111 (base 3) and 111 base 10 = 3 * 37.
a(12) = 40 because 40 (base 10) = 1111 (base 3) and 1111 base 10 = 11 * 101.
a(21) = 82 because 82 (base 10) = 10001 (base 3) and 10001 base 10 = 73 * 137.
a(26) = 100 because 100 (base 10) = 10201 (base 3) and 10201 base 10 = 101^2.
		

Crossrefs

Cf. A001358, A007089.

Cf. A110602 (base 4), A110603 (base 5), A110604 (base 6), A110605 (base 7) , A110606 (base 8), A110607 (base 9).

Programs

Maple

with(numtheory): a:=proc(n) local nn, nnn: nn:=convert(n,base,3): nnn:=add(nn[j]*10^(j-1),j=1..nops(nn)): if bigomega(nnn)=2 then n else fi end: seq(a(n),n=1..350); # Emeric Deutsch, Jul 16 2005

Mathematica

Select[Range[319], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 3]]] == 2 &] (* Ray Chandler, Sep 21 2005*)

Extensions

More terms from Emeric Deutsch, Jul 16 2005