A109024 Numbers that have exactly four prime factors counted with multiplicity (A014613) whose digit reversal is different and also has 4 prime factors (with multiplicity).

126, 225, 294, 315, 459, 488, 492, 513, 522, 558, 621, 650, 738, 837, 855, 884, 954, 1035, 1062, 1098, 1107, 1197, 1206, 1236, 1287, 1305, 1422, 1518, 1617, 1665, 1917, 1926, 1956, 1962, 1989, 2004, 2034, 2046, 2068, 2104, 2148, 2170, 2180, 2223, 2226

Offset: 1

Author

Jonathan Vos Post, Jun 16 2005

Keywords

• nonn
• base

Comments

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

Examples

			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.
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).
		

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's World of Mathematics, Emirpimes.

Crossrefs

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

Programs

Mathematica

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

PARI

is(n) = {
	my(r = fromdigits(Vecrev(digits(n))));
	n!=r && bigomega(n) == 4 && bigomega(r) == 4
} \\ David A. Corneth, Mar 07 2024