Search: id:A061906
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%I A061906
%S A061906 1,1,1,1,1,1,1,1,1,1,1,1,21,38,18,35,17,16,14,9,1,12,1,7,29,21,19,37,9,
%T A061906 8,1,14,66,1,8,15,7,3,13,15,1,16,6,23,1,13,9,3,44,7,1,19,13,4,518,1,11,
%U A061906 3,4,13,1,442,7,4,33,9,1,11,4,6,1,845,88,4,3,7,287,1,11,6,1,12345679,8
%N A061906 Obtain m by omitting trailing zeros from n; a(n) = smallest k such that 
               k*m is a palindrome.
%C A061906 Every positive integer is a factor of a palindrome, unless it is a multiple 
               of 10 (D. G. Radcliffe, see Links).
%C A061906 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 A061906 P. De Geest, <a href="http://www.worldofnumbers.com/em36.htm">Smallest 
               multipliers to make a number palindromic</a>.
%e A061906 For n = 30 we have m = 3, 1*m = 3 is a palindrome, so a(30) = 1. For 
               n = m = 12 the smallest palindromic multiple is 21*m = 252, so a(12) 
               = 21.
%o A061906 (ARIBAS): stop := 20000000; 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(k,
               " "); else write(-1," "); end; end;
%Y A061906 Cf. A050782, A062293, A061915, A061916, A061816. Values of k*m are given 
               in A061906.
%Y A061906 Sequence in context: A083567 A109211 A050782 this_sequence A139768 A072708 
               A102478
%Y A061906 Adjacent sequences: A061903 A061904 A061905 this_sequence A061907 A061908 
               A061909
%K A061906 base,easy,nonn
%O A061906 0,13
%A A061906 Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 25 2001

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