A109024 - OEIS

%I #33 Sep 03 2024 01:57:20

%S 126,225,294,315,459,488,492,513,522,558,621,650,738,837,855,884,954,

%T 1035,1062,1098,1107,1197,1206,1236,1287,1305,1422,1518,1617,1665,

%U 1917,1926,1956,1962,1989,2004,2034,2046,2068,2104,2148,2170,2180,2223,2226

%N Numbers that have exactly four prime factors counted with multiplicity (A014613) whose digit reversal is different and also has 4 prime factors (with multiplicity).

%C This sequence is the k = 4 instance of the series which begins with k = 1, k = 2, k = 3 (A109023).

%H David A. Corneth, <a href="/A109024/b109024.txt">Table of n, a(n) for n = 1..10000</a>

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

%e a(1) = 126 is in this sequence because 126 = 2 * 3^2 * 7 is a 4-almost prime and reverse(126) = 621 = 3^3 * 23 is also a 4-almost prime.

%e a(2) = 225 is in this sequence because 225 = 3^2 * 5^2 is a 4-almost prime and reverse(225) = 522 = 2 * 3^2 * 29 is also a 4-almost prime. (That 225 and 522 are concatenated from entirely prime digits is a coincidence, as with 2223).

%t Select[Range[2226],PrimeOmega[#]==4 && PrimeOmega[FromDigits[Reverse[IntegerDigits[#]]]]==4 &&!PalindromeQ[#]&] (* _James C. McMahon_, Mar 07 2024 *)

%o (PARI) is(n) = {

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

%o 	n!=r && bigomega(n) == 4 && bigomega(r) == 4

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

%Y Cf. A006567, A097393, A109018, A109023, A109025, A109026, A109027, A109028, A109029, A109030, A109031.

%K nonn,base

%O 1,1

%A _Jonathan Vos Post_, Jun 16 2005