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A118064
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Decimal expansion of the sum of the reciprocals of the palindromic primes A002385 (Honaker's constant).
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2
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1, 3, 2, 3, 9, 8, 2, 1, 4, 6, 8, 0, 6
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OFFSET
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1,2
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COMMENTS
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n \ sum to 10^n
02 1.267099567099567099567099567099567099567099567099567099567099567099567
03 1.320723244590290964212793334437872849720871258315369002493912638038324
05 1.323748402250648554164425746280035962754669829327727800040192015109270
07 1.323964105671202458016249150576217276147952428601889817773483085610332
09 1.323980718065525060936354534562000413901564393192688451911141729415146
11 1.323982026479475203850120990923294207966175748395470136325039323549015
13 1.323982136437462724794656629740867909978221153827990721566573347887836
15 1.323982145891606234777299440047139038371441916546100653011463101470839
17 1.323982146724859090645464845257681674740147563533254654075059843860490
19 1.323982146799188851138232927173756400348958236915409881890097448921521
21 1.323982146805857558347279363344557427339916178257233985191868031567947 (End)
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LINKS
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FORMULA
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Equals Sum_{p} 1/p, where p ranges over the palindromic primes.
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EXAMPLE
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1.323982146806...
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MATHEMATICA
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(* first obtain nextPalindrome from A007632 *) s = 1/11; c = 1; pp = 1; Do[ While[pp < 10^n, If[PrimeQ@ pp, c++; s = N[s + 1/pp, 64]]; pp = NextPalindrome@ pp]; If[ OddQ@ n, pp = 10^(n + 1); Print[{s, n, c}]], {n, 17}] (* Robert G. Wilson v, May 31 2009 *)
generate[n_] := Block[{id = IntegerDigits@n, insert = {{0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}}}, FromDigits@ Join[id, #, Reverse@ id] & /@ insert]; sm = N[Plus @@ (1/{2, 3, 5, 7, 11}), 64]; k = 1; Do [While[k < 10^n, sm = N[sm + Plus @@ (1/Select[ generate@k, PrimeQ]), 128]; k++ ]; Print[{2 n + 1, sm}], {n, 9}] (* Robert G. Wilson v, Nov 01 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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