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A061674 Smallest k such that k*n is a palindrome or becomes a palindrome when 0's are added on the left. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A089795 A081971 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

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Last modified March 26 20:47 EDT 2019. Contains 321535 sequences. (Running on oeis4.)