OFFSET
1,2
COMMENTS
From Robert G. Wilson v, Nov 01 2010: (Start)
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)
LINKS
Carlos Rivera, Problems & Puzzles: Puzzle 056 - Honaker's Constant.
Eric Weisstein, Palindromic Prime.
FORMULA
Equals Sum_{p} 1/p, where p ranges over the palindromic primes.
EXAMPLE
1.323982146806...
MATHEMATICA
(* 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 *)
CROSSREFS
KEYWORD
AUTHOR
Martin Renner, May 11 2006
EXTENSIONS
Corrected by Eric W. Weisstein, May 14 2006
More terms from Robert G. Wilson v, Nov 01 2010
Entry revised by N. J. A. Sloane, May 05 2013
STATUS
approved