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%I #13 Feb 15 2015 16:32:19
%S 0,2,2,6,4,20,6,686,8,666,20,22,60,2002,686,60,80,646,666,646,20,6006,
%T 22,828,600,200,2002,8886888,868,464,60,868,800,66,646,6860,828,222,
%U 646,6006,40,22222,6006,68886,44,6660,828,282,4224,686,200,42024,4004,424,8886888,220,8008,68286,464,68086,60
%N Smallest multiple k*n of n which has even digits and is a palindrome or becomes a palindrome when 0's are added on the left (e.g., 10 becomes 010, which is a palindrome).
%C Every integer n has a multiple of the form 99...9900...00. To see that n has a multiple that's a palindrome (allowing 0's on the left) with even digits, let 9n divide 99...9900...00; then n divides 22...2200...00. - _Dean Hickerson_, Jun 29 2001
%e a(7) = 686 as 686 = 98*7 is the smallest palindrome multiple of 7 with even digits.
%o (ARIBAS): stop := 500000; for n := 0 to 60 do k := 1; test := true; while test and k < stop do m := omit_trailzeros(n*k); if test := not all_even(m) or m <> int_reverse(m) then inc(k); end; end; if k < stop then write(n*k," "); else write(-1," "); end; end;
%o (Haskell)
%o a062293 0 = 0
%o a062293 n = head [x | x <- map (* n) [1..],
%o all (`elem` "02468") $ show x, a136522 (a004151 x) == 1]
%o -- _Reinhard Zumkeller_, Feb 01 2012
%Y Cf. A062279. Values of k are given in A061797.
%Y Cf. A014263, A136522, A004151.
%K nonn,base,easy
%O 0,2
%A _Amarnath Murthy_, Jun 18 2001
%E Corrected and extended by _Klaus Brockhaus_, Jun 21 2001
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