A118064 Decimal expansion of the sum of the reciprocals of the palindromic primes A002385 (Honaker's constant).

1, 3, 2, 3, 9, 8, 2, 1, 4, 6, 8, 0, 6

Offset: 1

Author

Martin Renner, May 11 2006

Keywords

• cons
• base
• nonn
• hard
• more

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)

Examples

			1.323982146806...
		

Links

• Carlos Rivera, Problems & Puzzles: Puzzle 056 - Honaker's Constant.
• Eric Weisstein, Palindromic Prime.

Crossrefs

Cf. A002385, A160910, A181442, A050251, A118031, A194097.

Programs

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 *)

Formula

Equals Sum_{p} 1/p, where p ranges over the palindromic primes.

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