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 A119684 Ternary emirpimes. 2
 112, 211, 1021, 1102, 1201, 2011, 2022, 2202, 10111, 11101, 11112, 12102, 12202, 12212, 20121, 20212, 20221, 21111, 21202, 21221, 100102, 100201, 101011, 101122, 101221, 102001, 102002, 102012, 102022, 102122, 102222, 110101, 110102, 110122, 110211, 111102, 111202, 112011, 112121, 112122, 112202 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 Eric Weisstein, Jonathan Vos Post, et al., Emirpimes. Eric Weisstein, Vincenzo Origlio, et al., Ternary. 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. 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. MAPLE R:= NULL: count:= 0: for m from 2 while count < 100 do for j from 1 to 2 while count < 100 do   n:= 3*m+j;   if numtheory:-bigomega(n) <> 2 then next fi;   L:= convert(n, base, 3);   r:= add(L[-i]*3^(i-1), i=1..nops(L));   if r <> n and numtheory:-bigomega(r) = 2 then      count:= count+1; R:= R, add(L[i]*10^(i-1), i=1..nops(L))   fi od od: R; # Robert Israel, Jun 07 2020 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, Dec 22 2010 *) CROSSREFS Cf. A001358, A004086, A007089, A097393. Sequence in context: A061281 A336329 A217149 * A235887 A296579 A297970 Adjacent sequences:  A119681 A119682 A119683 * A119685 A119686 A119687 KEYWORD base,easy,nonn AUTHOR Jonathan Vos Post, Jun 08 2006 EXTENSIONS More terms from Robert Israel, Jun 07 2020 STATUS approved

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Last modified January 24 14:40 EST 2021. Contains 340411 sequences. (Running on oeis4.)