A109027 Numbers that have exactly seven prime factors counted with multiplicity (A046308) whose digit reversal is different and also has 7 prime factors (with multiplicity).

8820, 21240, 21708, 21780, 21920, 23280, 23472, 23625, 23800, 25560, 25584, 25758, 26280, 27432, 27504, 27888, 27900, 28836, 29250, 29403, 29736, 29970, 30492, 34884, 36828, 40338, 40572, 40950, 41976, 42228, 42984, 43659, 43956, 44128

Offset: 1

Author

Jonathan Vos Post, Jun 16 2005

Keywords

• nonn
• base

Comments

This sequence is the k = 7 instance of the series which begins with k = 1 (emirps), k = 2, k = 3, k = 4, k = 5 (A109025), k = 6 (A109026).

Examples

			a(20) = 29403 is in this sequence because 29403 = 3^5 * 11^2 has exactly 7 prime factors counted with multiplicity and reverse(29403) = 30492 = 2^2 * 3^2 * 7 * 11^2 also has exactly 7 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. A046308, A006567, A097393, A109018, A109023, A109024, A109025, A109026, A109028, A109029, A109030, A109031.

Programs

Mathematica

Select[Range[45000],!PalindromeQ[#]&&PrimeOmega[#]==PrimeOmega[ IntegerReverse[ #]] ==7&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 02 2019 *)

PARI

is(n) = {
	my(r = fromdigits(Vecrev(digits(n))));
	n!=r && bigomega(n) == 7 && bigomega(r) == 7
} \\ David A. Corneth, Mar 07 2024