

A189484


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


0



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
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OFFSET

1,2


COMMENTS

This is to semiprimes A001358 as A046447 is to primes A000040.
The initial 1 represents the empty product.


LINKS

Table of n, a(n) for n=1..55.


EXAMPLE

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).


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 *)


CROSSREFS

Cf. A001358, A002113, A046328, A046447, A097393, A158126 Products of emirpimes pairs, sorted.
Sequence in context: A266346 A181018 A155569 * A155567 A225377 A036667
Adjacent sequences: A189481 A189482 A189483 * A189485 A189486 A189487


KEYWORD

nonn,base


AUTHOR

Jonathan Vos Post, Apr 22 2011


EXTENSIONS

Additional terms from Franklin T. AdamsWatters, Apr 28 2011
More terms from Giovanni Resta, Sep 15 2018


STATUS

approved



