A109023 3-almost primes (A014612) whose digit reversal is different and also has 3 prime factors (with multiplicity).

117, 147, 165, 244, 246, 285, 286, 290, 338, 366, 369, 406, 418, 425, 435, 438, 442, 475, 498, 506, 507, 508, 524, 534, 539, 548, 561, 574, 582, 604, 605, 609, 628, 642, 663, 670, 682, 705, 711, 741, 759, 805, 814, 826, 833, 834, 845, 890, 894, 906, 935

Offset: 1

Author

Jonathan Vos Post, Jun 16 2005

Keywords

• nonn
• base

Comments

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

Examples

			1066 is in this sequence because 1066 = 2 * 13 * 41, making it a 3-almost prime and reverse(1066) = 6601 = 7 * 23 * 41, also a 3-almost prime.
2001 is in this sequence because 2001 = 3 * 23 * 29 and reverse(2001) = 1002 = 2 * 3 * 167.
		

References

• W. W. R. Ball and H. S. M. Coxeter, Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 14-15, 1987.
• J. Edalj, Problem 1622. L'Intermédiaire des Mathématiciens, 16, 34, 1909.

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• J. Jonesco, Query 1622, L'Intermédiaire des Mathématiciens, 200, Tome VI, 1899.
• Eric Weisstein's World of Mathematics, Almost Prime.
• Eric Weisstein's World of Mathematics, Emirp.
• Eric Weisstein and Jonathan Vos Post, Emirpimes.

Crossrefs

Cf. A006567, A097393, A109018, A109024, A109025, A109026, A109027, A109028, A109029, A109030, A109031.

Programs

Mathematica

Select[Range[1000],PrimeOmega[#]==3&&PrimeOmega[FromDigits[Reverse[IntegerDigits[#]]]]==3&&!PalindromeQ[#]&] (* James C. McMahon, Mar 06 2024 *)

PARI

is(n) = {
	my(r = fromdigits(Vecrev(digits(n))));
	n!=r && bigomega(n) == 3 && bigomega(r) == 3
} \\ David A. Corneth, Mar 07 2024

Extensions

1002 replaced by 935 - R. J. Mathar, Dec 14 2009