A109030 Numbers that have exactly ten prime factors counted with multiplicity (A046314) whose digit reversal is different and also has 10 prime factors (with multiplicity).

46848, 84864, 217152, 219456, 232848, 251712, 257664, 259776, 274104, 276048, 401472, 415584, 422820, 428160, 428736, 447360, 466752, 485514, 637824, 650160, 654912, 677952, 808320, 840672, 846369, 848232, 963648

Offset: 1

Author

Jonathan Vos Post, Jun 16 2005

Keywords

• nonn
• base

Comments

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).

Examples

			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.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Almost Prime.
• Eric Weisstein's World of Mathematics, Emirp.
• Eric Weisstein and Jonathan Vos Post, Emirpimes.

Crossrefs

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

Programs

Mathematica

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 *)

PARI

is(n) = {
	my(r = fromdigits(Vecrev(digits(n))));
	n!=r && bigomega(n) == 10 && bigomega(r) == 10
} \\ David A. Corneth, Mar 07 2024