A062279 Smallest multiple k*n of n which is a palindrome or becomes a palindrome when 0's are added on the left (e.g. 10 becomes 010 which is a palindrome).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 60, 494, 70, 30, 80, 272, 90, 171, 20, 252, 22, 161, 600, 50, 494, 999, 252, 232, 30, 434, 800, 33, 272, 70, 252, 111, 494, 585, 40, 656, 252, 989, 44, 90, 414, 141, 2112, 343, 50, 969, 676, 212, 9990, 55, 616, 171, 232, 767

Offset: 0

Author

Amarnath Murthy, Jun 17 2001

Keywords

• nonn
• base
• easy
• nice

Comments

Every positive integer is a factor of a palindrome, unless it is a multiple of 10 (D. G. Radcliffe, see Links).

Examples

			a(13) = 494 is the smallest multiple of 13 which is a palindrome.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• P. De Geest, Smallest multipliers to make a number palindromic.

Crossrefs

Cf. A050782, A062293. Values of k are given in A061674.

Cf. A141709.

Programs

ARIBAS

: maxarg := 60; stop := 200000; for n := 0 to maxarg do k := 1; test := true; while test and k < stop do m := omit_trailzeros(n*k); if test := m <> int_reverse(m) then inc(k); end; end; if k < stop then write(n*k," "); else write(-1," "); end; end;

Haskell

a062279 0 = 0
a062279 n = until ((== 1) . a136522 . a004151) (+ n) n
-- Reinhard Zumkeller, May 06 2013

Formula

A136522(A004151(a(n))) = 1. - Reinhard Zumkeller, May 06 2013

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org) and Klaus Brockhaus, Jun 18 2001