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A061674 Smallest k such that k*n is a palindrome or becomes a palindrome when 0's are added on the left.

%I A061674 #17 Mar 24 2025 13:49:17
%S A061674 1,1,1,1,1,1,1,1,1,1,1,1,5,38,5,2,5,16,5,9,1,12,1,7,25,2,19,37,9,8,1,
%T A061674 14,25,1,8,2,7,3,13,15,1,16,6,23,1,2,9,3,44,7,1,19,13,4,185,1,11,3,4,
%U A061674 13,1,442,7,4,33,9,1,11,4,6,1,845,35,4,3,4,65,1,11,6,1,12345679,8,9,3
%N A061674 Smallest k such that k*n is a palindrome or becomes a palindrome when 0's are added on the left.
%C A061674 Every positive integer is a factor of a palindrome, unless it is a multiple of 10 (D. G. Radcliffe, see Links).
%H A061674 Reinhard Zumkeller, <a href="/A061674/b061674.txt">Table of n, a(n) for n = 0..2500</a>
%H A061674 Patrick De Geest, <a href="https://www.worldofnumbers.com/em36.htm">Smallest multipliers to make a number palindromic</a>.
%e A061674 a(12) = 5 since 5*12 = 60 (i.e. 060) is a palindrome.
%t A061674 rz[n_]:=Module[{idn=IntegerDigits[n]},While[Last[idn]==0,idn=Most[idn]];idn]; k[n_]:=Module[{k=1,p},p=k*n;While[rz[p]!=Reverse[rz[p]],k++;p=k*n];k]; Join[ {1},Array[k,90]] (* _Harvey P. Dale_, Mar 06 2013 *)
%o A061674 (ARIBAS) stop := 50000000; for n := 0 to 100 do k := 1; test := true; while test and k < stop do m := omit_trailzeros(n*k); if test := m <> int_reverse(m) then inc(k); end; end; if k < stop then write(k," "); else write(-1," "); end; end;
%o A061674 (Haskell)
%o A061674 a061674 n = until ((== 1) . a136522 . a004151 . (* n)) (+ 1) 1
%o A061674 -- _Reinhard Zumkeller_, Jul 20 2012
%Y A061674 Cf. A050782, A062293. Values of k*n are given in A062279.
%K A061674 nonn,base,easy,nice
%O A061674 0,13
%A A061674 _Amarnath Murthy_, Jun 17 2001