A109030 - OEIS

%I #25 Feb 16 2025 08:32:58

%S 46848,84864,217152,219456,232848,251712,257664,259776,274104,276048,

%T 401472,415584,422820,428160,428736,447360,466752,485514,637824,

%U 650160,654912,677952,808320,840672,846369,848232,963648

%N Numbers that have exactly ten prime factors counted with multiplicity (A046314) whose digit reversal is different and also has 10 prime factors (with multiplicity).

%C This sequence is the k = 10 instance of the series which begins with k = 1 (emirps), k = 2, k = 3 (A109023), k = 4 (A109024), k = 5 (A109025), k = 6 (A109026), k = 7 (A109027), k = 8 (A109028), k = 9 (A109029).

%H David A. Corneth, <a href="/A109030/b109030.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%e a(1) = 46848 is in this sequence because 46848 = 2^8 * 3 * 61 has exactly 10 prime factors counted with multiplicity and reverse(46848) = 84864 = 2^7 * 3 * 13 * 17 also has exactly 10 prime factors counted with multiplicity.

%t taQ[n_]:=Module[{idn=IntegerDigits[n],rev},rev=Reverse[idn];rev!=idn&&PrimeOmega[n] == 10 == PrimeOmega[FromDigits[rev]]]; Select[Range[ 1000000], taQ] (* _Harvey P. Dale_, May 03 2013 *)

%o (PARI) is(n) = {

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

%o 	n!=r && bigomega(n) == 10 && bigomega(r) == 10

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

%Y Cf. A046314, A006567, A097393, A109018, A109023, A109024, A109025, A109026, A109027, A109028, A109029, A109031.

%K nonn,base

%O 1,1

%A _Jonathan Vos Post_, Jun 16 2005