A061915 Obtain m by omitting trailing zeros from n; a(n) = smallest multiple k*m which is a palindrome with even digits, or -1 if no such multiple exists.

0, 2, 2, 6, 4, -1, 6, 686, 8, 666, 2, 22, 444, 2002, 686, -1, 464, 646, 666, 646, 2, 6006, 22, 828, 888, -1, 2002, 8886888, 868, 464, 6, 868, 4224, 66, 646, -1, 828, 222, 646, 6006, 4, 22222, 6006, 68886, 44, -1, 828, 282, 4224, 686, -1, 42024, 4004, 424, 8886888, -1, 8008, 68286, 464, 68086, 6

Offset: 0

Author

Klaus Brockhaus, Jun 25 2001

Keywords

• base
• sign
• easy

Comments

a(n) = -1 if and only if m ends with the digit 5.

Examples

			For n = 30 we have m = 3; 3*2 = 6 is a palindrome with even digits, so a(30) = 6.
		

Links

• P. De Geest, Smallest multipliers to make a number palindromic.

Crossrefs

Cf. A050782, A062293, A061816, A061906. Values of k are given in A061916.

Programs

ARIBAS

stop := 500000; for n := 0 to 60 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(mp," "); else write(-1," "); end; end;