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

0,13

Comments

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..2500

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A081971 A350966 A086877 * A247709 A097276 A280437

Adjacent sequences: A061671 A061672 A061673 * A061675 A061676 A061677

Keyword

nonn,base,easy,nice

Author

Amarnath Murthy, Jun 17 2001

Status

approved