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A110819 Non-palindromes in A110751; that is, non-palindromic numbers n such that n and R(n) have the same prime divisors, where R(n) = digit reversal of n.

%I A110819 #14 Dec 07 2019 12:18:25
%S A110819 1089,2178,4356,6534,8712,9801,10989,21978,24024,26208,42042,43956,
%T A110819 48048,61248,65934,80262,84084,84216,87912,98901,109989,219978,231504,
%U A110819 234234,242424,253344,255528,264264,272646,275184,277816,288288,405132,424242,432432,439956
%N A110819 Non-palindromes in A110751; that is, non-palindromic numbers n such that n and R(n) have the same prime divisors, where R(n) = digit reversal of n.
%C A110819 Trivially, if integer k is a term of this sequence, then R(k) is a term as well.
%C A110819 If n is in the sequence, then so is (10^m+1)*n where 10^m > n.  In particular, the sequence is infinite. - _Robert Israel_, Aug 14 2014
%H A110819 Donovan Johnson, <a href="/A110819/b110819.txt">Table of n, a(n) for n = 1..500</a>
%e A110819 The prime divisors of 87912 and R(87912) = 21978 are both {2, 3, 11, 37}, so 87912 and 21978 are both in the sequence.
%p A110819 revdigs:= proc(n)
%p A110819 local L,nL,i;
%p A110819 L:= convert(n,base,10);
%p A110819 nL:= nops(L);
%p A110819 add(L[i]*10^(nL-i),i=1..nL);
%p A110819 end:
%p A110819 filter:= proc(n) local r;
%p A110819   r:= revdigs(n);
%p A110819   r <> n and numtheory:-factorset(r) = numtheory:-factorset(n)
%p A110819 end proc:
%p A110819 select(filter, [$10 .. 10^6]); # _Robert Israel_, Aug 14 2014
%t A110819 r[n_] := FromDigits[Reverse[IntegerDigits[n]]]; Do[If[r[n] != n && Select[Divisors[n], PrimeQ] == Select[Divisors[r[n]], PrimeQ], Print[n]], {n, 1, 10^6}]
%o A110819 (Python)
%o A110819 from sympy import primefactors
%o A110819 A110819 = [n for n in range(1,10**6) if str(n) != str(n)[::-1] and primefactors(n) == primefactors(int(str(n)[::-1]))] # _Chai Wah Wu_, Aug 14 2014
%Y A110819 Cf. A110751.
%K A110819 base,nonn
%O A110819 1,1
%A A110819 _Ryan Propper_, Sep 15 2005