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Search: id:A061797
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| A061797 |
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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. |
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+0
2
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| 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
(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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LINKS
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P. De Geest, Smallest multipliers to make a number palindromic.
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EXAMPLE
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a(12) = 5 since 5*12 = 60 (i.e. 060) is a palindrome.
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PROGRAM
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(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;
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CROSSREFS
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Cf. A050782, A062293 A061674. Values of k*n are given in A062293.
Sequence in context: A067044 A055684 A024559 this_sequence A068341 A100380 A082399
Adjacent sequences: A061794 A061795 A061796 this_sequence A061798 A061799 A061800
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KEYWORD
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nonn,base,easy,nice
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 17 2001
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EXTENSIONS
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More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 27 2001
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