cp's OEIS Frontend

A061916 Obtain m by omitting trailing zeros from n; a(n) = smallest k such that k*m is a palindrome with even digits, or -1 if no such multiple exists.

%I A061916 #7 Feb 13 2025 21:15:15
%S A061916 1,2,1,2,1,-1,1,98,1,74,2,2,37,154,49,-1,29,38,37,34,1,286,1,36,37,-1,
%T A061916 77,329144,31,16,2,28,132,2,19,-1,23,6,17,154,1,542,143,1602,1,-1,18,
%U A061916 6,88,14,-1,824,77,8,164572,-1,143,1198,8,1154,1,1126,14,962,66,-1,1,998,121,12,98,65984,592,274,3,-1,529,26,77,358
%N A061916 Obtain m by omitting trailing zeros from n; a(n) = smallest k such that k*m is a palindrome with even digits, or -1 if no such multiple exists.
%C A061916 a(n) = -1 if and only if m ends with the digit 5.
%H A061916 P. De Geest, <a href="https://www.worldofnumbers.com/em36.htm">Smallest multipliers to make a number palindromic</a>.
%e A061916 For n = 30 we have m = 3; 3*2 = 6 is a palindrome with even digits, so a(30) = 2.
%o A061916 (ARIBAS) stop := 500000; for n := 0 to 80 do k := 1; test := true; while test and k < stop do mp := omit_trailzeros(n)*k; if test := not all_even(mp) or mp <> int_reverse(mp) then inc(k); end; end; if k < stop then write(k," "); else write(-1," "); end; end;
%Y A061916 Cf. A050782, A062293, A061816, A061906. Values of k*m are given in A061915.
%K A061916 base,easy,sign
%O A061916 0,2
%A A061916 _Klaus Brockhaus_, Jun 25 2001