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Search: id:A108873
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| A108873 |
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Numbers n whose base 3 representations, interpreted as base 10 integers, are semiprimes. |
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+0
7
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A110602 is the equivalent using base 4. 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.
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EXAMPLE
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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.
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MAPLE
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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); (Deutsch)
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MATHEMATICA
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Select[Range[319], Plus @@ Last /@ FactorInteger[FromDigits[IntegerDigits[ #, 3]]] == 2 &] (*Chandler*)
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CROSSREFS
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Cf. A001358, A007089, A110602, A110603, A110604, A110605, A110606, A110607.
Sequence in context: A050014 A132017 A010342 this_sequence A002312 A106474 A127441
Adjacent sequences: A108870 A108871 A108872 this_sequence A108874 A108875 A108876
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KEYWORD
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base,easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 13 2005
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 16 2005
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