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

1,1

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

Links

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

Example

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

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}]

Prog

(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

Crossrefs

Cf. A110751.

Sequence in context: A223429 A168661 A175698 * A071685 A008919 A110843

Adjacent sequences: A110816 A110817 A110818 * A110820 A110821 A110822

Keyword

base,nonn

Author

Ryan Propper, Sep 15 2005

Status

approved