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

0,2

Comments

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

Links

Table of n, a(n) for n=0..79.

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

Example

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

Prog

(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;

Crossrefs

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

Sequence in context: A264969 A320301 A324510 * A351819 A076348 A263835

Adjacent sequences: A061913 A061914 A061915 * A061917 A061918 A061919

Keyword

base,easy,sign

Author

Klaus Brockhaus, Jun 25 2001

Status

approved