A061674 Smallest k such that k*n is a palindrome or becomes a palindrome when 0's are added on the left.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 38, 5, 2, 5, 16, 5, 9, 1, 12, 1, 7, 25, 2, 19, 37, 9, 8, 1, 14, 25, 1, 8, 2, 7, 3, 13, 15, 1, 16, 6, 23, 1, 2, 9, 3, 44, 7, 1, 19, 13, 4, 185, 1, 11, 3, 4, 13, 1, 442, 7, 4, 33, 9, 1, 11, 4, 6, 1, 845, 35, 4, 3, 4, 65, 1, 11, 6, 1, 12345679, 8, 9, 3

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(12) = 5 since 5*12 = 60 (i.e. 060) is a palindrome.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..2500
• Patrick De Geest, Smallest multipliers to make a number palindromic.

Crossrefs

Cf. A050782, A062293. Values of k*n are given in A062279.

Programs

ARIBAS

stop := 50000000; for n := 0 to 100 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(k," "); else write(-1," "); end; end;

Haskell

a061674 n = until ((== 1) . a136522 . a004151 . (* n)) (+ 1) 1
-- Reinhard Zumkeller, Jul 20 2012

Mathematica

rz[n_]:=Module[{idn=IntegerDigits[n]},While[Last[idn]==0,idn=Most[idn]];idn]; k[n_]:=Module[{k=1,p},p=k*n;While[rz[p]!=Reverse[rz[p]],k++;p=k*n];k]; Join[ {1},Array[k,90]] (* Harvey P. Dale, Mar 06 2013 *)