A189484 Numbers that can be factored into semiprimes which, when concatenated in increasing order, produce a palindrome.

1, 4, 6, 9, 16, 22, 33, 36, 55, 56, 64, 77, 81, 111, 121, 136, 141, 156, 161, 202, 216, 256, 262, 276, 296, 303, 323, 351, 376, 393, 441, 454, 484, 505, 515, 516, 535, 545, 560, 565, 621, 626, 707, 717, 729, 737, 765, 767, 784, 818, 838, 878, 898, 939, 949

Offset: 1

Author

Jonathan Vos Post, Apr 22 2011

Keywords

• nonn
• base

Comments

This is to semiprimes A001358 as A046447 is to primes A000040.

The initial 1 represents the empty product.

Examples

			The first value not itself a semiprime palindrome (A046328) or power of semiprimes (i.e., 16 = 4 * 4 which concatenate to the palindrome 44, 484 = 22^2) is 56 = 4 * 14. The first where additionally the first factor is not a single digit is 765 = 15 * 51 = 3^2 * 5 * 17 since (15, 51) are a pair of emirpimes A097393, and 765 = A158126(1).
		

Crossrefs

Cf. A001358, A002113, A046328, A046447, A097393, A158126 Products of emirpimes pairs, sorted.

Programs

Mathematica

ok[n_] := n == 1 || Block[{d, p = Join @@ mu /@ FactorInteger[n]}, EvenQ@ Length[p] && AnyTrue[ Union[ Sort /@ ((Times @@@ #) & /@ Union[ (Sort /@ Partition[#, 2]) & /@ Permutations[p]])], (d = Join @@ IntegerDigits[#]; d == Reverse[d]) &]]; Select[ Range[1000], ok] (* Giovanni Resta, Sep 15 2018 *)

Extensions

Additional terms from Franklin T. Adams-Watters, Apr 28 2011

More terms from Giovanni Resta, Sep 15 2018