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A118031
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Decimal expansion of the sum of the reciprocals of the palindromic numbers A002113.
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5
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3, 3, 7, 0, 2, 8, 3, 2, 5, 9, 4, 9, 7, 3, 7, 3, 3, 2, 0, 4, 9, 2, 1, 5, 7, 2, 9, 8, 5, 0, 5, 5, 3, 1, 1, 2, 3, 0, 7, 1, 4, 5, 7, 7, 7, 9, 4, 5, 2, 7, 7, 8, 4, 9, 1, 3, 3, 5, 0, 6, 8, 9, 2, 5, 9, 8, 2, 5, 1, 9, 7, 6, 0, 3, 4, 9, 4, 7, 6, 7, 5, 8, 9, 7, 0, 3, 0, 1
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OFFSET
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1,1
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COMMENTS
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The sum using all palindromic numbers < 10^8 is 3.37000183240... Extrapolating using Wynn's epsilon method gives a value near 3.37018... - Eric W. Weisstein, May 14 2006
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LINKS
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FORMULA
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a(n) = Sum_{palindromes p>0} 1/p.
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EXAMPLE
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3.3702832594973733204921572985...
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MATHEMATICA
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NextPalindrome[n_] := Block[{l = Floor[ Log[10, n] + 1], idn = IntegerDigits@ n}, If[ Union@ idn == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[ idn, Ceiling[l/2]]]] > FromDigits[ Take[idn, -Ceiling[l/2]]], FromDigits[Join[Take[idn, Ceiling[l/2]], Reverse[Take[idn, Floor[l/2]]]]], idfhn = FromDigits[Take[idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits@ idfhn, Drop[ Reverse[ IntegerDigits@ idfhn], Mod[l, 2]]]]]]]]; pal = 1; sm = 0; Do[ While[pal < 10^n + 1, sm = N[sm + 1/pal, 128]; pal = NextPalindrome@ pal]; Print[{n, sm}], {n, 0, 17}] (* Robert G. Wilson v, Oct 20 2010 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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