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Numbers that can be factored into semiprimes which, when concatenated in increasing order, produce a palindrome.
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%I #18 Feb 16 2020 00:57:54

%S 1,4,6,9,16,22,33,36,55,56,64,77,81,111,121,136,141,156,161,202,216,

%T 256,262,276,296,303,323,351,376,393,441,454,484,505,515,516,535,545,

%U 560,565,621,626,707,717,729,737,765,767,784,818,838,878,898,939,949

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

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

%C The initial 1 represents the empty product.

%e 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).

%t 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 *)

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

%K nonn,base

%O 1,2

%A _Jonathan Vos Post_, Apr 22 2011

%E Additional terms from _Franklin T. Adams-Watters_, Apr 28 2011

%E More terms from _Giovanni Resta_, Sep 15 2018