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A118031 Decimal expansion of the sum of the reciprocals of the palindromic numbers A002113. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 W. Weisstein, May 14 2006

LINKS

Joseph Myers, Table of n, a(n) for n = 1..1001

Joseph Myers, Polynomial-time algorithm.

Eric Weisstein: Palindromic Number.

FORMULA

a(n) = sum(1/p), p is a palindrome.

EXAMPLE

3.3702832594973733204921572985...

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, Oct 20 2010*)

CROSSREFS

Cf. A002113.

Similar sequences: A118064, A194097, A244162.

Sequence in context: A221688 A066358 A114187 * A240504 A235162 A059527

Adjacent sequences:  A118028 A118029 A118030 * A118032 A118033 A118034

KEYWORD

cons,base,nonn

AUTHOR

Martin Renner, May 11 2006

EXTENSIONS

Corrected by Eric W. Weisstein, May 14 2006

Corrected and more terms by Robert G. Wilson v, Oct 20 2010

Corrected and extended by Joseph Myers, Jun 26 2014

STATUS

approved

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Last modified November 28 19:08 EST 2014. Contains 250399 sequences.