

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
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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^(i1), i=1..nops(L));
if r <> n and numtheory:bigomega(r) = 2 then
count:= count+1; R:= R, add(L[i]*10^(i1), 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: A336329 A349206 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



