Search: id:A061816
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%I A061816
%S A061816 0,1,2,3,4,5,6,7,8,9,1,11,252,494,252,525,272,272,252,171,2,252,22,161,
%T A061816 696,525,494,999,252,232,3,434,2112,33,272,525,252,111,494,585,4,656,
%U A061816 252,989,44,585,414,141,2112,343,5,969,676,212,27972,55,616,171,232
%N A061816 Obtain m by omitting trailing zeros from n (cf. A004151); a(n) = smallest 
               multiple k*m which is a palindrome.
%C A061816 Every positive integer is a factor of a palindrome, unless it is a multiple 
               of 10 (D. G. Radcliffe, see links).
%C A061816 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.
%H A061816 P. De Geest, <a href="http://www.worldofnumbers.com/em36.htm">Smallest 
               multipliers to make a number palindromic</a>.
%e A061816 For n = 30 we have m = 3, 1*m = 3 is a palindrome, so a(30) = 3. For 
               n = m = 12 the smallest palindromic multiple is 21*m = 252, so a(12) 
               = 252.
%o A061816 (ARIBAS): stop := 200000; for n := 0 to maxarg do k := 1; test := true; 
               while test and k < stop do mp := omit_trailzeros(n)*k; if test := 
               mp <> int_reverse(mp) then inc(k); end; end; if k < stop then write(mp,
               " "); else write(-1," "); end; end;
%Y A061816 Cf. A050782, A062293, A061915, A061916. Values of k are given in A061906.
%Y A061816 Sequence in context: A084011 A004086 A121760 this_sequence A083960 A138795 
               A093017
%Y A061816 Adjacent sequences: A061813 A061814 A061815 this_sequence A061817 A061818 
               A061819
%K A061816 base,easy,nonn
%O A061816 0,3
%A A061816 Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 25 2001

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