Search: id:A062293
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%I A062293
%S A062293 0,2,2,6,4,20,6,686,8,666,20,22,60,2002,686,60,80,646,666,646,20,6006,
               22,828,600,200,2002,8886888,868,
%T A062293 464,60,868,800,66,646,6860,828,222,646,6006,40,22222,6006,68886,44,6660,
               828,282,4224,686,200,42024,
%U A062293 4004,424,8886888,220,8008,68286,464,68086,60
%N A062293 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 A062293 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 A062293 a(7) = 686 as 686 = 98*7 is the smallest palindrome multiple of 7 with 
               even digits.
%o A062293 (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;
%Y A062293 Cf. A062279. Values of k are given in A061797.
%Y A062293 Sequence in context: A083467 A061807 A062885 this_sequence A054516 A062400 
               A064766
%Y A062293 Adjacent sequences: A062290 A062291 A062292 this_sequence A062294 A062295 
               A062296
%K A062293 nonn,base,easy
%O A062293 0,2
%A A062293 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 18 2001
%E A062293 Corrected and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 
               Jun 21 2001

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