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

1,1

Links

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

Example

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.

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*)

Crossrefs

Cf. A001358, A007089.

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

Sequence in context: A132017 A244592 A010342 * A002312 A252496 A279517

Adjacent sequences: A108870 A108871 A108872 * A108874 A108875 A108876

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Jul 13 2005

Extensions

More terms from Emeric Deutsch, Jul 16 2005

Status

approved