cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A189484 #18 Feb 16 2020 00:57:54
%S A189484 1,4,6,9,16,22,33,36,55,56,64,77,81,111,121,136,141,156,161,202,216,
%T A189484 256,262,276,296,303,323,351,376,393,441,454,484,505,515,516,535,545,
%U A189484 560,565,621,626,707,717,729,737,765,767,784,818,838,878,898,939,949
%N A189484 Numbers that can be factored into semiprimes which, when concatenated in increasing order, produce a palindrome.
%C A189484 This is to semiprimes A001358 as A046447 is to primes A000040.
%C A189484 The initial 1 represents the empty product.
%e A189484 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 A189484 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 A189484 Cf. A001358, A002113, A046328, A046447, A097393, A158126 Products of emirpimes pairs, sorted.
%K A189484 nonn,base
%O A189484 1,2
%A A189484 _Jonathan Vos Post_, Apr 22 2011
%E A189484 Additional terms from _Franklin T. Adams-Watters_, Apr 28 2011
%E A189484 More terms from _Giovanni Resta_, Sep 15 2018