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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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0
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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, 0, 9, 7, 4, 3
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The sum using all palindromic numbers <10^8 is 3.37000183240... Extrapolating using Wynn's epsilon method gives a value near 3.37018... - Eric Weisstein (eric(AT)weisstein.com), May 14 2006
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LINKS
| Eric Weisstein: Palindromic Number.
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FORMULA
| a(n) = sum(1/p), p is a palindrome.
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EXAMPLE
| 3.37028325949737332049209743...
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MATHEMATICA
| 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 (rgwv(AT)rgwv.com), Oct 20 2010*)
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CROSSREFS
| Cf. A002113.
Sequence in context: A103895 A066358 A114187 * A059527 A101457 A076217
Adjacent sequences: A118028 A118029 A118030 * A118032 A118033 A118034
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KEYWORD
| cons,base,nonn,more
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AUTHOR
| Martin Renner (martin.renner(AT)gmx.net), May 11 2006
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EXTENSIONS
| Corrected by Eric Weisstein (eric(AT)weisstein.com), May 14 2006.
Corrected and more terms by Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 20 2010.
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