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A062293 Smallest multiple k*n of n which has even digits and is a palindrome or becomes a palindrome when 0's are added on the left (e.g., 10 becomes 010, which is a palindrome). 8
0, 2, 2, 6, 4, 20, 6, 686, 8, 666, 20, 22, 60, 2002, 686, 60, 80, 646, 666, 646, 20, 6006, 22, 828, 600, 200, 2002, 8886888, 868, 464, 60, 868, 800, 66, 646, 6860, 828, 222, 646, 6006, 40, 22222, 6006, 68886, 44, 6660, 828, 282, 4224, 686, 200, 42024, 4004, 424, 8886888, 220, 8008, 68286, 464, 68086, 60 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Every integer n has a multiple of the form 99...9900...00. To see that n has a multiple that's a palindrome (allowing 0's on the left) with even digits, let 9n divide 99...9900...00; then n divides 22...2200...00. - Dean Hickerson, Jun 29 2001

LINKS

Table of n, a(n) for n=0..60.

EXAMPLE

a(7) = 686 as 686 = 98*7 is the smallest palindrome multiple of 7 with even digits.

PROG

(ARIBAS): stop := 500000; for n := 0 to 60 do k := 1; test := true; while test and k < stop do m := omit_trailzeros(n*k); if test := not all_even(m) or m <> int_reverse(m) then inc(k); end; end; if k < stop then write(n*k, " "); else write(-1, " "); end; end;

(Haskell)

a062293 0 = 0

a062293 n = head [x | x <- map (* n) [1..],

                 all (`elem` "02468") $ show x, a136522 (a004151 x) == 1]

-- Reinhard Zumkeller, Feb 01 2012

CROSSREFS

Cf. A062279. Values of k are given in A061797.

Cf. A014263, A136522, A004151.

Sequence in context: A083467 A061807 A062885 * A317368 A259882 A204991

Adjacent sequences:  A062290 A062291 A062292 * A062294 A062295 A062296

KEYWORD

nonn,base,easy

AUTHOR

Amarnath Murthy, Jun 18 2001

EXTENSIONS

Corrected and extended by Klaus Brockhaus, Jun 21 2001

STATUS

approved

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Last modified November 17 12:09 EST 2018. Contains 317276 sequences. (Running on oeis4.)