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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 A261295 * 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 extended 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 May 27 03:03 EDT 2020. Contains 334647 sequences. (Running on oeis4.)