A109029 Numbers that have exactly nine prime factors counted with multiplicity (A046312) whose digit reversal is different and also has 9 prime factors (with multiplicity).

21168, 23424, 23616, 27456, 41184, 42432, 48114, 61632, 65472, 86112, 211410, 212256, 213192, 215232, 217440, 219072, 230208, 232512, 236925, 236928, 238656, 238680, 251100, 251505, 251748, 253824, 255024, 255960, 257856, 259968, 270912

Offset

1,1

Comments

This sequence is the k = 8 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).

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.

Example

a(1) = 21168 is in this sequence because 21168 = 2^4 * 3^3 * 7^2 has exactly 9 prime factors counted with multiplicity and reverse(21168) = 86112 = 2^5 * 3^2 * 13 * 23 also has exactly 9 prime factors counted with multiplicity.

Mathematica

okQ[n_]:=Module[{idn=IntegerDigits[n], ridn}, ridn=Reverse[idn]; idn!=ridn && PrimeOmega[n]==9&&PrimeOmega[FromDigits[ridn]]==9]; Select[Range[ 271000], okQ] (* Harvey P. Dale, Sep 24 2011 *)

Prog

(PARI) is(n) = {
	my(r = fromdigits(Vecrev(digits(n))));
	n!=r && bigomega(n) == 9 && bigomega(r) == 9
} \\ David A. Corneth, Mar 07 2024

Crossrefs

Cf. A046312, A006567, A097393, A109018, A109023, A109024, A109025, A109026, A109027, A109028, A109030, A109031.

Sequence in context: A294059 A255949 A273659 * A284915 A252165 A289674

Adjacent sequences: A109026 A109027 A109028 * A109030 A109031 A109032

Keyword

nonn,base,changed

Author

Jonathan Vos Post, Jun 16 2005

Status

approved