

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
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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, Polynomialtime 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



