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
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
KEYWORD
base,easy,nonn
AUTHOR
Jonathan Vos Post, Jun 08 2006
EXTENSIONS
More terms from Robert Israel, Jun 07 2020
STATUS
approved