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.

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, 77, 329144, 31, 16, 2, 28, 132, 2, 19, -1, 23, 6, 17, 154, 1, 542, 143, 1602, 1, -1, 18, 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

Offset: 0

Author

Klaus Brockhaus, Jun 25 2001

Keywords

• base
• easy
• sign

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) = 2.
		

Links

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

Crossrefs

Cf. A050782, A062293, A061816, A061906. Values of k*m are given in A061915.

Programs

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;