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A119684
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Ternary emirpimes.
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1
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112, 211, 1021, 1102, 1201, 2011, 2022, 2202, 10111, 11101, 11112, 12102, 12202, 12212, 20121, 20212, 20221
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| These are semiprimes when read as base 3 numbers and their reversals are different semiprimes when read as base 3 numbers. Base 10 these are: 14, 22, 34, 38, 46, 58, 62, 74, 94, 118, 122, 146, 155, 158, 178, 185, 187, ... See: A097393 Emirpimes: numbers n such that n and its reversal are distinct semiprimes. See: A004086 Read n backwards (referred to as R(n) in many sequences). See: A007089 Numbers in base 3.
Apparently numbers with trailing zeros (reversed with leading zeros), like 1220 and 10020, are not included. - R. J. Mathar, Dec 22 2010
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LINKS
| Eric Weisstein, Jonathan Vos Post, et al., Emirpimes.
Eric Weisstein, Vincenzo Origlio, et al., Ternary.
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FORMULA
| a(n) = A007089(i) for some i in A001358 and R(a(n)) = A007089(j) for some j =/= i in A001358. a(n) = A007089(i) for some i in A001358 and A004086(a(n)) = A007089(j) for some j =/= i in A001358.
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EXAMPLE
| a(1) = 112 because 112 (base 3) = 14 (base 10) is semiprime and R(112) = 211, where 211 (base 3) = 22 (base 10) is a different semiprime.
a(13) = 12202 because 12202 (base 3) = 155 (base 10) is semiprime and R(12202) = 20221, where 20221 (base 3) = 187 (base 10) is a different semiprime.
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MATHEMATICA
| (* First run the program for A105999 *) SemiPrimeQ[n_Integer] := TrueQ[SemiPrimePi[n] > SemiPrimePi[n - 1]]; BaseForm[Select[Table[SemiPrime[n], {n, 100}], GCD[#, 3] == 1 && # != FromDigits[Reverse[IntegerDigits[#, 3]], 3] && SemiPrimeQ[FromDigits[Reverse[IntegerDigits[#, 3]], 3]] &], 3] (* From Alonso del Arte, alonso.delarte(AT)gmail.com, Dec 22 2010 *)
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CROSSREFS
| Cf. A001358, A004086, A007089, A097393.
Sequence in context: A157662 A095615 A061281 * A203923 A203916 A189544
Adjacent sequences: A119681 A119682 A119683 * A119685 A119686 A119687
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KEYWORD
| base,easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 08 2006
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