%I #11 Jul 19 2023 20:30:42

%S 1469,9641,13273,14339,15613,15769,15899,16913,31651,31961,34193,

%T 37231,39143,39299,93341,96751,99293,99851,115373,124639,135713,

%U 143039,157469,159913,317531,319951,341093,373511,390143,392899,930341,936421,964751

%N Composite n such that both n and its reversal in base 10 are squarefree, none of the prime factors of n are palindromes and the prime factors of the reversal of n are the reversals of those of n.

%C Many trivial terms are obtained if one drops the requirement that none of the prime factors of n be palindromes.

%C If n is in the sequence, so is its reversal. The smallest palindrome in the sequence is 1226221 = 1021 * 1201.

%C All terms up to 5000000 have just 2 prime factors and the digits of the prime factors are all 0, 1, 2, or 3. Is this true for all terms?

%e 1469 is the product of two distinct non-palindromic primes: 1469 = 13 * 113 and reverse(1469) = 9641 has prime factorization 9641 = reverse(13) * reverse(113) = 31 * 311. Hence 1469 belongs to the sequence.

%t rev[n_] := FromDigits[Reverse[IntegerDigits[n]]]; pal[n_] := n==rev[n]; For[n=2, True, n++, ps=First/@(fn=FactorInteger[n]); If[Length[fn]>1&&Max@@Last/@fn==1&&!Or@@pal/@ps&&And@@PrimeQ/@rev/@ps&&Times@@rev/@ps==rev[n], Print[n]]];

%K nonn,base

%O 1,1

%A _Joseph L. Pe_, Jun 09 2003

%E Edited by _Dean Hickerson_, Jun 12 2003