A109023 - OEIS

%I #31 Mar 28 2024 23:38:34

%S 117,147,165,244,246,285,286,290,338,366,369,406,418,425,435,438,442,

%T 475,498,506,507,508,524,534,539,548,561,574,582,604,605,609,628,642,

%U 663,670,682,705,711,741,759,805,814,826,833,834,845,890,894,906,935

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

%C This sequence is the k = 3 instance of the series which begins with k = 1, k = 2.

%D W. W. R. Ball and H. S. M. Coxeter, Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 14-15, 1987.

%D J. Edalj, Problem 1622. L'Intermédiaire des Mathématiciens, 16, 34, 1909.

%H David A. Corneth, <a href="/A109023/b109023.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Emirp.html">Emirp</a>.

%H Eric Weisstein and Jonathan Vos Post, <a href="http://mathworld.wolfram.com/Emirpimes.html">Emirpimes.</a>

%e 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 2001 is in this sequence because 2001 = 3 * 23 * 29 and reverse(2001) = 1002 = 2 * 3 * 167.

%t Select[Range[1000],PrimeOmega[#]==3&&PrimeOmega[FromDigits[Reverse[IntegerDigits[#]]]]==3&&!PalindromeQ[#]&] (* _James C. McMahon_, Mar 06 2024 *)

%o (PARI) is(n) = {

%o 	my(r = fromdigits(Vecrev(digits(n))));

%o 	n!=r && bigomega(n) == 3 && bigomega(r) == 3

%o } \\ _David A. Corneth_, Mar 07 2024

%Y Cf. A006567, A097393, A109018, A109024, A109025, A109026, A109027, A109028, A109029, A109030, A109031.

%K nonn,base

%O 1,1

%A _Jonathan Vos Post_, Jun 16 2005

%E 1002 replaced by 935 - _R. J. Mathar_, Dec 14 2009