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%I #16 Jun 29 2015 12:44:30
%S 0,3,6,6,3,6,0,0,3,9,7,1,9,5,2,3,2,9,5,1,7,1,8,8,2,5,0,8,9,6,7,4,1,2,
%T 4,2,6,6,2,5,1,7,3,9,5,0,3,4,2,1,1,8,7,6,0,0,2,0,0,7,1,1,3,5,0,8,5,2,
%U 8,3,3,3,2,9,3,4,9,5,1,5,7,5,8,4,4,6,5
%N Decimal expansion of the sum of the reciprocal of the squares of the numbers whose digits are all even.
%C A rational approximation (correct up to the 9th decimal digit) is 22781/62182.
%C Continued fraction: [0, 2, 1, 2, 1, 2, 3, 3, 1, 8, 5, 2, 1, 14,...].
%e Decimal expansion of Sum_{k=1..oo}{1/A045926(k)^2} = 1/2^2 + 1/4^2 + 1/6^2 + 1/8^2 + 1/22^2 + 1/24^2 + 1/26^2 + ... = 0.3663600397195232951718825089674124266251739503421187600...
%p P:=proc(q) local a,b,k,ok,n; a:=0; for n from 2 by 2 to q do ok:=1; b:=n;
%p for k from 1 to ilog10(n)+1 do if (b mod 10)=0 or ((b mod 10) mod 2)=1 then ok:=0;
%p break; else b:=trunc(b/10); fi; od; if ok=1 then a:=a+(1/n)^2; fi; od;
%p print(evalf(a,200)); end: P(10^9);
%Y Cf. A045926, A194181, A194182.
%K nonn,cons
%O 1,2
%A _Paolo P. Lava_, May 25 2015
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