

A061797


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


2



1, 2, 1, 2, 1, 4, 1, 98, 1, 74, 2, 2, 5, 154, 49, 4, 5, 38, 37, 34, 1, 286, 1, 36, 25, 8, 77, 329144, 31, 16, 2, 28, 25, 2, 19, 196, 23, 6, 17, 154, 1, 542, 143, 1602, 1, 148, 18, 6, 88, 14, 4, 824, 77, 8, 164572, 4, 143, 1198, 8, 1154, 1, 1126, 14, 962, 66, 308, 1, 998
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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

Reinhard Zumkeller, Table of n, a(n) for n = 0..80
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

a[n_] := For[k = 1, True, k++, id = IntegerDigits[k*n]; If[AllTrue[id, EvenQ], rid = Reverse[id]; If[id == rid  (id //. {d__, 0} :> {d}) == (rid //. {0, d__} :> {d}), Return[k]]]]; a[0] = 1; Table[a[n], {n, 0, 70}] (* JeanFrançois Alcover, Apr 01 2016 *)


PROG

(ARIBAS): stop := 500000; for n := 0 to 75 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(k, " "); else write(1, " "); end; end;
(Haskell)
a061797 0 = 1
a061797 n = head [k  k < [1..], let x = k * n,
all (`elem` "02468") $ show x, a136522 (a004151 x) == 1]
 Reinhard Zumkeller, Feb 01 2012


CROSSREFS

Cf. A050782, A062293 A061674. Values of k*n are given in A062293.
Cf. A014263, A136522, A004151.
Sequence in context: A300584 A024559 A334664 * A068341 A321368 A338508
Adjacent sequences: A061794 A061795 A061796 * A061798 A061799 A061800


KEYWORD

nonn,base,easy,nice


AUTHOR

Amarnath Murthy, Jun 17 2001


EXTENSIONS

More terms from Klaus Brockhaus, Jun 27 2001


STATUS

approved



