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Search: id:A062293
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| A062293 |
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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). |
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8
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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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.
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EXAMPLE
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a(7) = 686 as 686 = 98*7 is the smallest palindrome multiple of 7 with even digits.
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PROGRAM
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(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;
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CROSSREFS
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Cf. A062279. Values of k are given in A061797.
Sequence in context: A083467 A061807 A062885 this_sequence A054516 A062400 A064766
Adjacent sequences: A062290 A062291 A062292 this_sequence A062294 A062295 A062296
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KEYWORD
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nonn,base,easy
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 18 2001
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EXTENSIONS
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Corrected and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 21 2001
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