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A023745
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Plaindromes: numbers whose digits in base 3 are in nondecreasing order.
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9
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0, 1, 2, 4, 5, 8, 13, 14, 17, 26, 40, 41, 44, 53, 80, 121, 122, 125, 134, 161, 242, 364, 365, 368, 377, 404, 485, 728, 1093, 1094, 1097, 1106, 1133, 1214, 1457, 2186, 3280, 3281, 3284, 3293, 3320, 3401, 3644, 4373, 6560, 9841, 9842, 9845, 9854
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OFFSET
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1,3
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LINKS
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FORMULA
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Numbers that in ternary are the concatenation of i 1's with j 2's, i, j>=0. Also a(n) = A073216(n+1) - 1. Proof: Write a(n) as 1{m}2{n}, then adding 1 gives 1{m-1}20{n} for m>0 and 10{n} for m=0. Doubling yields 10{m-1}10{n} or 20{n}, respectively. These two forms exactly describe the forms of sums of two powers of 3, the two powers being 3^n and 3^(m+n). - Hugo van der Sanden
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EXAMPLE
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In base 3 these numbers are 0, 1, 2, 11, 12, 22, 111, 112, 122, 222, 1111, 1112, ... [corrected by Sean A. Irvine, Jun 10 2019]
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MATHEMATICA
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Select[Range[0, 10000], !Negative[Min[Differences[IntegerDigits[ #, 3]]]]&] (* or *) With[{nn=10}, FromDigits[#, 3]&/@Union[Flatten[Table[ PadRight[ PadLeft[{}, n, 1], x, 2], {n, 0, nn}, {x, 0, nn}], 1]]] (* Harvey P. Dale, Oct 12 2011 *)
Select[Range[0, 10000], LessEqual@@IntegerDigits[#, 3]&] (* Ray Chandler, Jan 06 2014 *)
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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