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.

1089, 2178, 4356, 6534, 8712, 9801, 10989, 21978, 24024, 26208, 42042, 43956, 48048, 61248, 65934, 80262, 84084, 84216, 87912, 98901, 109989, 219978, 231504, 234234, 242424, 253344, 255528, 264264, 272646, 275184, 277816, 288288, 405132, 424242, 432432, 439956

Offset: 1

Author

Ryan Propper, Sep 15 2005

Keywords

• base
• nonn

Comments

Trivially, if integer k is a term of this sequence, then R(k) is a term as well.

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

Examples

			The prime divisors of 87912 and R(87912) = 21978 are both {2, 3, 11, 37}, so 87912 and 21978 are both in the sequence.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A110751.

Programs

Maple

revdigs:= proc(n)
local L,nL,i;
L:= convert(n,base,10);
nL:= nops(L);
add(L[i]*10^(nL-i),i=1..nL);
end:
filter:= proc(n) local r;
  r:= revdigs(n);
  r <> n and numtheory:-factorset(r) = numtheory:-factorset(n)
end proc:
select(filter, [$10 .. 10^6]); # Robert Israel, Aug 14 2014

Mathematica

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}]

Python

from sympy import primefactors
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