cp's OEIS Frontend

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).

%I A062293 #17 Mar 04 2025 14:49:43
%S A062293 0,2,2,6,4,20,6,686,8,666,20,22,60,2002,686,60,80,646,666,646,20,6006,
%T A062293 22,828,600,200,2002,8886888,868,464,60,868,800,66,646,6860,828,222,
%U A062293 646,6006,40,22222,6006,68886,44,6660,828,282,4224,686,200,42024,4004,424,8886888,220,8008,68286,464,68086,60
%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;
%o A062293 (Haskell)
%o A062293 a062293 0 = 0
%o A062293 a062293 n = head [x | x <- map (* n) [1..],
%o A062293                  all (`elem` "02468") $ show x, a136522 (a004151 x) == 1]
%o A062293 -- _Reinhard Zumkeller_, Feb 01 2012
%Y A062293 Cf. A062279. Values of k are given in A061797.
%Y A062293 Cf. A014263, A136522, A004151.
%K A062293 nonn,base,easy
%O A062293 0,2
%A A062293 _Amarnath Murthy_, Jun 18 2001
%E A062293 Corrected and extended by _Klaus Brockhaus_, Jun 21 2001