A083526 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.

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

Offset

1,1

Comments

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?

Links

Table of n, a(n) for n=1..33.

Example

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.

Mathematica

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]]];

Crossrefs

Sequence in context: A215849 A204871 A252578 * A068753 A255735 A252521

Adjacent sequences: A083523 A083524 A083525 * A083527 A083528 A083529

Keyword

nonn,base

Author

Joseph L. Pe, Jun 09 2003

Extensions

Edited by Dean Hickerson, Jun 12 2003

Status

approved