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A109023 3-almost primes (A014612) whose digit reversal is different and also has 3 prime factors (with multiplicity).

%I A109023 #32 Feb 16 2025 08:32:58
%S A109023 117,147,165,244,246,285,286,290,338,366,369,406,418,425,435,438,442,
%T A109023 475,498,506,507,508,524,534,539,548,561,574,582,604,605,609,628,642,
%U A109023 663,670,682,705,711,741,759,805,814,826,833,834,845,890,894,906,935
%N A109023 3-almost primes (A014612) whose digit reversal is different and also has 3 prime factors (with multiplicity).
%C A109023 This sequence is the k = 3 instance of the series which begins with k = 1, k = 2.
%D A109023 W. W. R. Ball and H. S. M. Coxeter, Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 14-15, 1987.
%D A109023 J. Edalj, Problem 1622. L'Intermédiaire des Mathématiciens, 16, 34, 1909.
%H A109023 David A. Corneth, <a href="/A109023/b109023.txt">Table of n, a(n) for n = 1..10000</a>
%H A109023 J. Jonesco, <a href="https://archive.org/details/lintermdiairede03lemogoog/page/200/mode/2up?view=theater">Query 1622</a>, L'Intermédiaire des Mathématiciens, 200, Tome VI, 1899.
%H A109023 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%H A109023 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Emirp.html">Emirp</a>.
%H A109023 Eric Weisstein and Jonathan Vos Post, <a href="https://mathworld.wolfram.com/Emirpimes.html">Emirpimes.</a>
%e A109023 1066 is in this sequence because 1066 = 2 * 13 * 41, making it a 3-almost prime and reverse(1066) = 6601 = 7 * 23 * 41, also a 3-almost prime.
%e A109023 2001 is in this sequence because 2001 = 3 * 23 * 29 and reverse(2001) = 1002 = 2 * 3 * 167.
%t A109023 Select[Range[1000],PrimeOmega[#]==3&&PrimeOmega[FromDigits[Reverse[IntegerDigits[#]]]]==3&&!PalindromeQ[#]&] (* _James C. McMahon_, Mar 06 2024 *)
%o A109023 (PARI) is(n) = {
%o A109023 	my(r = fromdigits(Vecrev(digits(n))));
%o A109023 	n!=r && bigomega(n) == 3 && bigomega(r) == 3
%o A109023 } \\ _David A. Corneth_, Mar 07 2024
%Y A109023 Cf. A006567, A097393, A109018, A109024, A109025, A109026, A109027, A109028, A109029, A109030, A109031.
%K A109023 nonn,base
%O A109023 1,1
%A A109023 _Jonathan Vos Post_, Jun 16 2005
%E A109023 1002 replaced by 935 - _R. J. Mathar_, Dec 14 2009