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A083526
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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.
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0
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1469, 9641, 13273, 14339, 15613, 15769, 15899, 16913, 31651, 31961, 34193, 37231, 39143, 39299, 93341, 96751, 99293, 99851, 115373, 124639, 135713, 143039, 157469, 159913, 317531, 319951, 341093, 373511, 390143, 392899, 930341, 936421, 964751
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OFFSET
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1,1
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COMMENTS
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Many trivial terms are obtained if one drops the requirement that none of the prime factors of n be palindromes.
If n is in the sequence, so is its reversal. The smallest palindrome in the sequence is 1226221 = 1021 * 1201.
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?
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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]]];
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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