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

1,1

Comments

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

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) = 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).

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A290203 A254370 A325932 * A249190 A356143 A254465

Adjacent sequences: A109021 A109022 A109023 * A109025 A109026 A109027

Keyword

nonn,base

Author

Jonathan Vos Post, Jun 16 2005

Status

approved