

A110819


Nonpalindromes in A110751; that is, nonpalindromic numbers n such that n and R(n) have the same prime divisors, where R(n) = digit reversal of n.


8



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
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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^(nLi), 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



