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%I #46 Oct 30 2022 15:06:28
%S 1,3,2,3,9,8,2,1,4,6,8,0,6
%N Decimal expansion of the sum of the reciprocals of the palindromic primes A002385 (Honaker's constant).
%C From _Robert G. Wilson v_, Nov 01 2010: (Start)
%C n \ sum to 10^n
%C 02 1.267099567099567099567099567099567099567099567099567099567099567099567
%C 03 1.320723244590290964212793334437872849720871258315369002493912638038324
%C 05 1.323748402250648554164425746280035962754669829327727800040192015109270
%C 07 1.323964105671202458016249150576217276147952428601889817773483085610332
%C 09 1.323980718065525060936354534562000413901564393192688451911141729415146
%C 11 1.323982026479475203850120990923294207966175748395470136325039323549015
%C 13 1.323982136437462724794656629740867909978221153827990721566573347887836
%C 15 1.323982145891606234777299440047139038371441916546100653011463101470839
%C 17 1.323982146724859090645464845257681674740147563533254654075059843860490
%C 19 1.323982146799188851138232927173756400348958236915409881890097448921521
%C 21 1.323982146805857558347279363344557427339916178257233985191868031567947 (End)
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_056.htm">Problems & Puzzles: Puzzle 056 - Honaker's Constant</a>.
%H Eric Weisstein, <a href="http://mathworld.wolfram.com/PalindromicPrime.html">Palindromic Prime</a>.
%F Equals Sum_{p} 1/p, where p ranges over the palindromic primes.
%e 1.323982146806...
%t (* 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 *)
%t 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 *)
%Y Cf. A002385, A160910, A181442, A050251, A118031, A194097.
%K cons,base,nonn,hard,more
%O 1,2
%A _Martin Renner_, May 11 2006
%E Corrected by _Eric W. Weisstein_, May 14 2006
%E More terms from _Robert G. Wilson v_, Nov 01 2010
%E Entry revised by _N. J. A. Sloane_, May 05 2013
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